Daily Papers

Masked modeling has emerged as a powerful self-supervised learning framework, but existing methods largely rely on random masking, disregarding the structural properties of different modalities. In this work, we introduce structured noise-based masking, a simple yet effective approach that naturally aligns with the spatial, temporal, and spectral characteristics of video and audio data. By filtering white noise into distinct color noise distributions, we generate structured masks that preserve modality-specific patterns without requiring handcrafted heuristics or access to the data. Our approach improves the performance of masked video and audio modeling frameworks without any computational overhead. Extensive experiments demonstrate that structured noise masking achieves consistent improvement over random masking for standard and advanced masked modeling methods, highlighting the importance of modality-aware masking strategies for representation learning.

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are increasingly replaced by data-driven deep generative models, and several groups have recently shown that state-of-the-art score-based diffusion models yield particularly strong performance and flexibility. In this paper, we show that the powerful paradigm of posterior sampling with diffusion models can be extended to include rich, structured, noise models. To that end, we propose a joint conditional reverse diffusion process with learned scores for the noise and signal-generating distribution. We demonstrate strong performance gains across various inverse problems with structured noise, outperforming competitive baselines that use normalizing flows and adversarial networks. This opens up new opportunities and relevant practical applications of diffusion modeling for inverse problems in the context of non-Gaussian measurement models.

Recent advancements in text-to-video (T2V) diffusion models have significantly enhanced the visual quality of the generated videos. However, even recent T2V models find it challenging to follow text descriptions accurately, especially when the prompt requires accurate control of spatial layouts or object trajectories. A recent line of research uses layout guidance for T2V models that require fine-tuning or iterative manipulation of the attention map during inference time. This significantly increases the memory requirement, making it difficult to adopt a large T2V model as a backbone. To address this, we introduce Video-MSG, a training-free Guidance method for T2V generation based on Multimodal planning and Structured noise initialization. Video-MSG consists of three steps, where in the first two steps, Video-MSG creates Video Sketch, a fine-grained spatio-temporal plan for the final video, specifying background, foreground, and object trajectories, in the form of draft video frames. In the last step, Video-MSG guides a downstream T2V diffusion model with Video Sketch through noise inversion and denoising. Notably, Video-MSG does not need fine-tuning or attention manipulation with additional memory during inference time, making it easier to adopt large T2V models. Video-MSG demonstrates its effectiveness in enhancing text alignment with multiple T2V backbones (VideoCrafter2 and CogVideoX-5B) on popular T2V generation benchmarks (T2VCompBench and VBench). We provide comprehensive ablation studies about noise inversion ratio, different background generators, background object detection, and foreground object segmentation.

Generative modeling aims to transform random noise into structured outputs. In this work, we enhance video diffusion models by allowing motion control via structured latent noise sampling. This is achieved by just a change in data: we pre-process training videos to yield structured noise. Consequently, our method is agnostic to diffusion model design, requiring no changes to model architectures or training pipelines. Specifically, we propose a novel noise warping algorithm, fast enough to run in real time, that replaces random temporal Gaussianity with correlated warped noise derived from optical flow fields, while preserving the spatial Gaussianity. The efficiency of our algorithm enables us to fine-tune modern video diffusion base models using warped noise with minimal overhead, and provide a one-stop solution for a wide range of user-friendly motion control: local object motion control, global camera movement control, and motion transfer. The harmonization between temporal coherence and spatial Gaussianity in our warped noise leads to effective motion control while maintaining per-frame pixel quality. Extensive experiments and user studies demonstrate the advantages of our method, making it a robust and scalable approach for controlling motion in video diffusion models. Video results are available on our webpage: https://vgenai-netflix-eyeline-research.github.io/Go-with-the-Flow. Source code and model checkpoints are available on GitHub: https://github.com/VGenAI-Netflix-Eyeline-Research/Go-with-the-Flow.

Generative models transform random noise into images; their inversion aims to transform images back to structured noise for recovery and editing. This paper addresses two key tasks: (i) inversion and (ii) editing of a real image using stochastic equivalents of rectified flow models (such as Flux). Although Diffusion Models (DMs) have recently dominated the field of generative modeling for images, their inversion presents faithfulness and editability challenges due to nonlinearities in drift and diffusion. Existing state-of-the-art DM inversion approaches rely on training of additional parameters or test-time optimization of latent variables; both are expensive in practice. Rectified Flows (RFs) offer a promising alternative to diffusion models, yet their inversion has been underexplored. We propose RF inversion using dynamic optimal control derived via a linear quadratic regulator. We prove that the resulting vector field is equivalent to a rectified stochastic differential equation. Additionally, we extend our framework to design a stochastic sampler for Flux. Our inversion method allows for state-of-the-art performance in zero-shot inversion and editing, outperforming prior works in stroke-to-image synthesis and semantic image editing, with large-scale human evaluations confirming user preference.

Latent Video Diffusion Models (LVDMs) achieve high-quality generation but are sensitive to imperfect conditioning, which causes semantic drift and temporal incoherence on noisy, web-scale video-text datasets. We introduce CAT-LVDM, the first corruption-aware training framework for LVDMs that improves robustness through structured, data-aligned noise injection. Our method includes Batch-Centered Noise Injection (BCNI), which perturbs embeddings along intra-batch semantic directions to preserve temporal consistency. BCNI is especially effective on caption-rich datasets like WebVid-2M, MSR-VTT, and MSVD. We also propose Spectrum-Aware Contextual Noise (SACN), which injects noise along dominant spectral directions to improve low-frequency smoothness, showing strong results on UCF-101. On average, BCNI reduces FVD by 31.9% across WebVid-2M, MSR-VTT, and MSVD, while SACN yields a 12.3% improvement on UCF-101. Ablation studies confirm the benefit of low-rank, data-aligned noise. Our theoretical analysis further explains how such perturbations tighten entropy, Wasserstein, score-drift, mixing-time, and generalization bounds. CAT-LVDM establishes a principled, scalable training approach for robust video diffusion under multimodal noise. Code and models: https://github.com/chikap421/catlvdm

Though Rectified Flows (ReFlows) with distillation offers a promising way for fast sampling, its fast inversion transforms images back to structured noise for recovery and following editing remains unsolved. This paper introduces FireFlow, a simple yet effective zero-shot approach that inherits the startling capacity of ReFlow-based models (such as FLUX) in generation while extending its capabilities to accurate inversion and editing in 8 steps. We first demonstrate that a carefully designed numerical solver is pivotal for ReFlow inversion, enabling accurate inversion and reconstruction with the precision of a second-order solver while maintaining the practical efficiency of a first-order Euler method. This solver achieves a 3times runtime speedup compared to state-of-the-art ReFlow inversion and editing techniques, while delivering smaller reconstruction errors and superior editing results in a training-free mode. The code is available at https://github.com/HolmesShuan/FireFlow{this URL}.

This paper proposes ConsistDreamer - a novel framework that lifts 2D diffusion models with 3D awareness and 3D consistency, thus enabling high-fidelity instruction-guided scene editing. To overcome the fundamental limitation of missing 3D consistency in 2D diffusion models, our key insight is to introduce three synergetic strategies that augment the input of the 2D diffusion model to become 3D-aware and to explicitly enforce 3D consistency during the training process. Specifically, we design surrounding views as context-rich input for the 2D diffusion model, and generate 3D-consistent, structured noise instead of image-independent noise. Moreover, we introduce self-supervised consistency-enforcing training within the per-scene editing procedure. Extensive evaluation shows that our ConsistDreamer achieves state-of-the-art performance for instruction-guided scene editing across various scenes and editing instructions, particularly in complicated large-scale indoor scenes from ScanNet++, with significantly improved sharpness and fine-grained textures. Notably, ConsistDreamer stands as the first work capable of successfully editing complex (e.g., plaid/checkered) patterns. Our project page is at immortalco.github.io/ConsistDreamer.

We propose a simple and novel method for generating 3D human motion from complex natural language sentences, which describe different velocity, direction and composition of all kinds of actions. Different from existing methods that use classical generative architecture, we apply the Denoising Diffusion Probabilistic Model to this task, synthesizing diverse motion results under the guidance of texts. The diffusion model converts white noise into structured 3D motion by a Markov process with a series of denoising steps and is efficiently trained by optimizing a variational lower bound. To achieve the goal of text-conditioned image synthesis, we use the classifier-free guidance strategy to fuse text embedding into the model during training. Our experiments demonstrate that our model achieves competitive results on HumanML3D test set quantitatively and can generate more visually natural and diverse examples. We also show with experiments that our model is capable of zero-shot generation of motions for unseen text guidance.

Knowledge-based visual question answering (VQA) involves answering questions that require external knowledge not present in the image. Existing methods first retrieve knowledge from external resources, then reason over the selected knowledge, the input image, and question for answer prediction. However, this two-step approach could lead to mismatches that potentially limit the VQA performance. For example, the retrieved knowledge might be noisy and irrelevant to the question, and the re-embedded knowledge features during reasoning might deviate from their original meanings in the knowledge base (KB). To address this challenge, we propose PICa, a simple yet effective method that Prompts GPT3 via the use of Image Captions, for knowledge-based VQA. Inspired by GPT-3's power in knowledge retrieval and question answering, instead of using structured KBs as in previous work, we treat GPT-3 as an implicit and unstructured KB that can jointly acquire and process relevant knowledge. Specifically, we first convert the image into captions (or tags) that GPT-3 can understand, then adapt GPT-3 to solve the VQA task in a few-shot manner by just providing a few in-context VQA examples. We further boost performance by carefully investigating: (i) what text formats best describe the image content, and (ii) how in-context examples can be better selected and used. PICa unlocks the first use of GPT-3 for multimodal tasks. By using only 16 examples, PICa surpasses the supervised state of the art by an absolute +8.6 points on the OK-VQA dataset. We also benchmark PICa on VQAv2, where PICa also shows a decent few-shot performance.

Echocardiography has been a prominent tool for the diagnosis of cardiac disease. However, these diagnoses can be heavily impeded by poor image quality. Acoustic clutter emerges due to multipath reflections imposed by layers of skin, subcutaneous fat, and intercostal muscle between the transducer and heart. As a result, haze and other noise artifacts pose a real challenge to cardiac ultrasound imaging. In many cases, especially with difficult-to-image patients such as patients with obesity, a diagnosis from B-Mode ultrasound imaging is effectively rendered unusable, forcing sonographers to resort to contrast-enhanced ultrasound examinations or refer patients to other imaging modalities. Tissue harmonic imaging has been a popular approach to combat haze, but in severe cases is still heavily impacted by haze. Alternatively, denoising algorithms are typically unable to remove highly structured and correlated noise, such as haze. It remains a challenge to accurately describe the statistical properties of structured haze, and develop an inference method to subsequently remove it. Diffusion models have emerged as powerful generative models and have shown their effectiveness in a variety of inverse problems. In this work, we present a joint posterior sampling framework that combines two separate diffusion models to model the distribution of both clean ultrasound and haze in an unsupervised manner. Furthermore, we demonstrate techniques for effectively training diffusion models on radio-frequency ultrasound data and highlight the advantages over image data. Experiments on both in-vitro and in-vivo cardiac datasets show that the proposed dehazing method effectively removes haze while preserving signals from weakly reflected tissue.

Hyperspectral Unmixing (HU) has received increasing attention in the past decades due to its ability of unveiling information latent in hyperspectral data. Unfortunately, most existing methods fail to take advantage of the spatial information in data. To overcome this limitation, we propose a Structured Sparse regularized Nonnegative Matrix Factorization (SS-NMF) method from the following two aspects. First, we incorporate a graph Laplacian to encode the manifold structures embedded in the hyperspectral data space. In this way, the highly similar neighboring pixels can be grouped together. Second, the lasso penalty is employed in SS-NMF for the fact that pixels in the same manifold structure are sparsely mixed by a common set of relevant bases. These two factors act as a new structured sparse constraint. With this constraint, our method can learn a compact space, where highly similar pixels are grouped to share correlated sparse representations. Experiments on real hyperspectral data sets with different noise levels demonstrate that our method outperforms the state-of-the-art methods significantly.

Automatic table detection in PDF documents has achieved a great success but tabular data extraction are still challenging due to the integrity and noise issues in detected table areas. The accurate data extraction is extremely crucial in finance area. Inspired by this, the aim of this research is proposing an automated table detection and tabular data extraction from financial PDF documents. We proposed a method that consists of three main processes, which are detecting table areas with a Faster R-CNN (Region-based Convolutional Neural Network) model with Feature Pyramid Network (FPN) on each page image, extracting contents and structures by a compounded layout segmentation technique based on optical character recognition (OCR) and formulating regular expression rules for table header separation. The tabular data extraction feature is embedded with rule-based filtering and restructuring functions that are highly scalable. We annotate a new Financial Documents dataset with table regions for the experiment. The excellent table detection performance of the detection model is obtained from our customized dataset. The main contributions of this paper are proposing the Financial Documents dataset with table-area annotations, the superior detection model and the rule-based layout segmentation technique for the tabular data extraction from PDF files.

Structured illumination microscopy (SIM) has become an important technique for optical super-resolution imaging because it allows a doubling of image resolution at speeds compatible for live-cell imaging. However, the reconstruction of SIM images is often slow and prone to artefacts. Here we propose a versatile reconstruction method, ML-SIM, which makes use of machine learning. The model is an end-to-end deep residual neural network that is trained on a simulated data set to be free of common SIM artefacts. ML-SIM is thus robust to noise and irregularities in the illumination patterns of the raw SIM input frames. The reconstruction method is widely applicable and does not require the acquisition of experimental training data. Since the training data are generated from simulations of the SIM process on images from generic libraries the method can be efficiently adapted to specific experimental SIM implementations. The reconstruction quality enabled by our method is compared with traditional SIM reconstruction methods, and we demonstrate advantages in terms of noise, reconstruction fidelity and contrast for both simulated and experimental inputs. In addition, reconstruction of one SIM frame typically only takes ~100ms to perform on PCs with modern Nvidia graphics cards, making the technique compatible with real-time imaging. The full implementation and the trained networks are available at http://ML-SIM.com.

Retrieval-augmented generation (RAG) enhances large language models (LLMs) by incorporating external knowledge. Current hybrid RAG system retrieves evidence from both knowledge graphs (KGs) and text documents to support LLM reasoning. However, it faces challenges like handling multi-hop reasoning, multi-entity questions, multi-source verification, and effective graph utilization. To address these limitations, we present Hydra, a training-free framework that unifies graph topology, document semantics, and source reliability to support deep, faithful reasoning in LLMs. Hydra handles multi-hop and multi-entity problems through agent-driven exploration that combines structured and unstructured retrieval, increasing both diversity and precision of evidence. To tackle multi-source verification, Hydra uses a tri-factor cross-source verification (source trustworthiness assessment, cross-source corroboration, and entity-path alignment), to balance topic relevance with cross-modal agreement. By leveraging graph structure, Hydra fuses heterogeneous sources, guides efficient exploration, and prunes noise early. Comprehensive experiments on seven benchmark datasets show that Hydra achieves overall state-of-the-art results on all benchmarks with GPT-3.5, outperforming the strong hybrid baseline ToG-2 by an average of 20.3% and up to 30.1%. Furthermore, Hydra enables smaller models (e.g., Llama-3.1-8B) to achieve reasoning performance comparable to that of GPT-4-Turbo.

Text-to-SQL, which involves translating natural language into Structured Query Language (SQL), is crucial for enabling broad access to structured databases without expert knowledge. However, designing models for such tasks is challenging due to numerous factors, including the presence of 'noise,' such as ambiguous questions and syntactical errors. This study provides an in-depth analysis of the distribution and types of noise in the widely used BIRD-Bench benchmark and the impact of noise on models. While BIRD-Bench was created to model dirty and noisy database values, it was not created to contain noise and errors in the questions and gold queries. We found that noise in questions and gold queries are prevalent in the dataset, with varying amounts across domains, and with an uneven distribution between noise types. The presence of incorrect gold SQL queries, which then generate incorrect gold answers, has a significant impact on the benchmark's reliability. Surprisingly, when evaluating models on corrected SQL queries, zero-shot baselines surpassed the performance of state-of-the-art prompting methods. We conclude that informative noise labels and reliable benchmarks are crucial to developing new Text-to-SQL methods that can handle varying types of noise. All datasets, annotations, and code are available at https://github.com/niklaswretblad/the-effects-of-noise-in-text-to-SQL.

We propose Samba ASR, the first state-of-the-art Automatic Speech Recognition (ASR) model leveraging the novel Mamba architecture as both encoder and decoder, built on the foundation of state-space models (SSMs). Unlike transformer-based ASR models, which rely on self-attention mechanisms to capture dependencies, Samba ASR effectively models both local and global temporal dependencies using efficient state-space dynamics, achieving remarkable performance gains. By addressing the limitations of transformers, such as quadratic scaling with input length and difficulty in handling long-range dependencies, Samba ASR achieves superior accuracy and efficiency. Experimental results demonstrate that Samba ASR surpasses existing open-source transformer-based ASR models across various standard benchmarks, establishing it as the new state of the art in ASR. Extensive evaluations on benchmark datasets show significant improvements in Word Error Rate (WER), with competitive performance even in low-resource scenarios. Furthermore, the computational efficiency and parameter optimization of the Mamba architecture make Samba ASR a scalable and robust solution for diverse ASR tasks. Our contributions include: A new Samba ASR architecture demonstrating the superiority of SSMs over transformer-based models for speech sequence processing. A comprehensive evaluation on public benchmarks showcasing state-of-the-art performance. An analysis of computational efficiency, robustness to noise, and sequence generalization. This work highlights the viability of Mamba SSMs as a transformer-free alternative for efficient and accurate ASR. By leveraging state-space modeling advancements, Samba ASR sets a new benchmark for ASR performance and future research.

In the U.S. historically, local newspapers drew their content largely from newswires like the Associated Press. Historians argue that newswires played a pivotal role in creating a national identity and shared understanding of the world, but there is no comprehensive archive of the content sent over newswires. We reconstruct such an archive by applying a customized deep learning pipeline to hundreds of terabytes of raw image scans from thousands of local newspapers. The resulting dataset contains 2.7 million unique public domain U.S. newswire articles, written between 1878 and 1977. Locations in these articles are georeferenced, topics are tagged using customized neural topic classification, named entities are recognized, and individuals are disambiguated to Wikipedia using a novel entity disambiguation model. To construct the Newswire dataset, we first recognize newspaper layouts and transcribe around 138 millions structured article texts from raw image scans. We then use a customized neural bi-encoder model to de-duplicate reproduced articles, in the presence of considerable abridgement and noise, quantifying how widely each article was reproduced. A text classifier is used to ensure that we only include newswire articles, which historically are in the public domain. The structured data that accompany the texts provide rich information about the who (disambiguated individuals), what (topics), and where (georeferencing) of the news that millions of Americans read over the course of a century. We also include Library of Congress metadata information about the newspapers that ran the articles on their front pages. The Newswire dataset is useful both for large language modeling - expanding training data beyond what is available from modern web texts - and for studying a diversity of questions in computational linguistics, social science, and the digital humanities.

We introduce MoCA-Video (Motion-Aware Concept Alignment in Video), a training-free framework bridging the gap between image-domain semantic mixing and video. Given a generated video and a user-provided reference image, MoCA-Video injects the semantic features of the reference image into a specific object within the video, while preserving the original motion and visual context. Our approach leverages a diagonal denoising schedule and class-agnostic segmentation to detect and track objects in the latent space and precisely control the spatial location of the blended objects. To ensure temporal coherence, we incorporate momentum-based semantic corrections and gamma residual noise stabilization for smooth frame transitions. We evaluate MoCA's performance using the standard SSIM, image-level LPIPS, temporal LPIPS, and introduce a novel metric CASS (Conceptual Alignment Shift Score) to evaluate the consistency and effectiveness of the visual shifts between the source prompt and the modified video frames. Using self-constructed dataset, MoCA-Video outperforms current baselines, achieving superior spatial consistency, coherent motion, and a significantly higher CASS score, despite having no training or fine-tuning. MoCA-Video demonstrates that structured manipulation in the diffusion noise trajectory allows for controllable, high-quality video synthesis.

Within the ambit of VoIP (Voice over Internet Protocol) telecommunications, the complexities introduced by acoustic transformations merit rigorous analysis. This research, rooted in the exploration of proprietary sender-side denoising effects, meticulously evaluates platforms such as Google Meets and Zoom. The study draws upon the Deep Noise Suppression (DNS) 2020 dataset, ensuring a structured examination tailored to various denoising settings and receiver interfaces. A methodological novelty is introduced via Blinder-Oaxaca decomposition, traditionally an econometric tool, repurposed herein to analyze acoustic-phonetic perturbations within VoIP systems. To further ground the implications of these transformations, psychoacoustic metrics, specifically PESQ and STOI, were used to explain of perceptual quality and intelligibility. Cumulatively, the insights garnered underscore the intricate landscape of VoIP-influenced acoustic dynamics. In addition to the primary findings, a multitude of metrics are reported, extending the research purview. Moreover, out-of-domain benchmarking for both time and time-frequency domain speech enhancement models is included, thereby enhancing the depth and applicability of this inquiry.

In this work, we address dynamic view synthesis from monocular videos as an inverse problem in a training-free setting. By redesigning the noise initialization phase of a pre-trained video diffusion model, we enable high-fidelity dynamic view synthesis without any weight updates or auxiliary modules. We begin by identifying a fundamental obstacle to deterministic inversion arising from zero-terminal signal-to-noise ratio (SNR) schedules and resolve it by introducing a novel noise representation, termed K-order Recursive Noise Representation. We derive a closed form expression for this representation, enabling precise and efficient alignment between the VAE-encoded and the DDIM inverted latents. To synthesize newly visible regions resulting from camera motion, we introduce Stochastic Latent Modulation, which performs visibility aware sampling over the latent space to complete occluded regions. Comprehensive experiments demonstrate that dynamic view synthesis can be effectively performed through structured latent manipulation in the noise initialization phase.

The personalized dialogue explores the consistent relationship between dialogue generation and personality. Existing personalized dialogue agents model persona profiles from three resources: sparse or dense persona descriptions and dialogue histories. However, sparse structured persona attributes are explicit but uninformative, dense persona texts contain rich persona descriptions with much noise, and dialogue history query is both noisy and uninformative for persona modeling. In this work, we combine the advantages of the three resources to obtain a richer and more accurate persona. We design a Contrastive Latent Variable-based model (CLV) that clusters the dense persona descriptions into sparse categories, which are combined with the history query to generate personalized responses. Experimental results on Chinese and English datasets demonstrate our model's superiority in personalization.

Image editing has advanced significantly with the development of diffusion models using both inversion-based and instruction-based methods. However, current inversion-based approaches struggle with big modifications (e.g., adding or removing objects) due to the structured nature of inversion noise, which hinders substantial changes. Meanwhile, instruction-based methods often constrain users to black-box operations, limiting direct interaction for specifying editing regions and intensity. To address these limitations, we propose BrushEdit, a novel inpainting-based instruction-guided image editing paradigm, which leverages multimodal large language models (MLLMs) and image inpainting models to enable autonomous, user-friendly, and interactive free-form instruction editing. Specifically, we devise a system enabling free-form instruction editing by integrating MLLMs and a dual-branch image inpainting model in an agent-cooperative framework to perform editing category classification, main object identification, mask acquisition, and editing area inpainting. Extensive experiments show that our framework effectively combines MLLMs and inpainting models, achieving superior performance across seven metrics including mask region preservation and editing effect coherence.

In this work, we propose DiffWave, a versatile diffusion probabilistic model for conditional and unconditional waveform generation. The model is non-autoregressive, and converts the white noise signal into structured waveform through a Markov chain with a constant number of steps at synthesis. It is efficiently trained by optimizing a variant of variational bound on the data likelihood. DiffWave produces high-fidelity audios in different waveform generation tasks, including neural vocoding conditioned on mel spectrogram, class-conditional generation, and unconditional generation. We demonstrate that DiffWave matches a strong WaveNet vocoder in terms of speech quality (MOS: 4.44 versus 4.43), while synthesizing orders of magnitude faster. In particular, it significantly outperforms autoregressive and GAN-based waveform models in the challenging unconditional generation task in terms of audio quality and sample diversity from various automatic and human evaluations.

Retrieval-augmented Generation (RAG) enhances Large Language Models (LLMs) by integrating external knowledge to reduce hallucinations and incorporate up-to-date information without retraining. As an essential part of RAG, external knowledge bases are commonly built by extracting structured data from unstructured PDF documents using Optical Character Recognition (OCR). However, given the imperfect prediction of OCR and the inherent non-uniform representation of structured data, knowledge bases inevitably contain various OCR noises. In this paper, we introduce OHRBench, the first benchmark for understanding the cascading impact of OCR on RAG systems. OHRBench includes 350 carefully selected unstructured PDF documents from six real-world RAG application domains, along with Q&As derived from multimodal elements in documents, challenging existing OCR solutions used for RAG To better understand OCR's impact on RAG systems, we identify two primary types of OCR noise: Semantic Noise and Formatting Noise and apply perturbation to generate a set of structured data with varying degrees of each OCR noise. Using OHRBench, we first conduct a comprehensive evaluation of current OCR solutions and reveal that none is competent for constructing high-quality knowledge bases for RAG systems. We then systematically evaluate the impact of these two noise types and demonstrate the vulnerability of RAG systems. Furthermore, we discuss the potential of employing Vision-Language Models (VLMs) without OCR in RAG systems. Code: https://github.com/opendatalab/OHR-Bench

We deal with the combinatorial problem of learning directed acyclic graph (DAG) structure from observational data adhering to a linear structural equation model (SEM). Leveraging advances in differentiable, nonconvex characterizations of acyclicity, recent efforts have advocated a continuous constrained optimization paradigm to efficiently explore the space of DAGs. Most existing methods employ lasso-type score functions to guide this search, which (i) require expensive penalty parameter retuning when the unknown SEM noise variances change across problem instances; and (ii) implicitly rely on limiting homoscedasticity assumptions. In this work, we propose a new convex score function for sparsity-aware learning of linear DAGs, which incorporates concomitant estimation of scale and thus effectively decouples the sparsity parameter from the exogenous noise levels. Regularization via a smooth, nonconvex acyclicity penalty term yields CoLiDE (Concomitant Linear DAG Estimation), a regression-based criterion amenable to efficient gradient computation and closed-form estimation of noise variances in heteroscedastic scenarios. Our algorithm outperforms state-of-the-art methods without incurring added complexity, especially when the DAGs are larger and the noise level profile is heterogeneous. We also find CoLiDE exhibits enhanced stability manifested via reduced standard deviations in several domain-specific metrics, underscoring the robustness of our novel linear DAG estimator.

This paper proposes a shape anchor guided learning strategy (AncLearn) for robust holistic indoor scene understanding. We observe that the search space constructed by current methods for proposal feature grouping and instance point sampling often introduces massive noise to instance detection and mesh reconstruction. Accordingly, we develop AncLearn to generate anchors that dynamically fit instance surfaces to (i) unmix noise and target-related features for offering reliable proposals at the detection stage, and (ii) reduce outliers in object point sampling for directly providing well-structured geometry priors without segmentation during reconstruction. We embed AncLearn into a reconstruction-from-detection learning system (AncRec) to generate high-quality semantic scene models in a purely instance-oriented manner. Experiments conducted on the challenging ScanNetv2 dataset demonstrate that our shape anchor-based method consistently achieves state-of-the-art performance in terms of 3D object detection, layout estimation, and shape reconstruction. The code will be available at https://github.com/Geo-Tell/AncRec.

Controllable layout generation aims at synthesizing plausible arrangement of element bounding boxes with optional constraints, such as type or position of a specific element. In this work, we try to solve a broad range of layout generation tasks in a single model that is based on discrete state-space diffusion models. Our model, named LayoutDM, naturally handles the structured layout data in the discrete representation and learns to progressively infer a noiseless layout from the initial input, where we model the layout corruption process by modality-wise discrete diffusion. For conditional generation, we propose to inject layout constraints in the form of masking or logit adjustment during inference. We show in the experiments that our LayoutDM successfully generates high-quality layouts and outperforms both task-specific and task-agnostic baselines on several layout tasks.

We propose to restore old photos that suffer from severe degradation through a deep learning approach. Unlike conventional restoration tasks that can be solved through supervised learning, the degradation in real photos is complex and the domain gap between synthetic images and real old photos makes the network fail to generalize. Therefore, we propose a novel triplet domain translation network by leveraging real photos along with massive synthetic image pairs. Specifically, we train two variational autoencoders (VAEs) to respectively transform old photos and clean photos into two latent spaces. And the translation between these two latent spaces is learned with synthetic paired data. This translation generalizes well to real photos because the domain gap is closed in the compact latent space. Besides, to address multiple degradations mixed in one old photo, we design a global branch with apartial nonlocal block targeting to the structured defects, such as scratches and dust spots, and a local branch targeting to the unstructured defects, such as noises and blurriness. Two branches are fused in the latent space, leading to improved capability to restore old photos from multiple defects. Furthermore, we apply another face refinement network to recover fine details of faces in the old photos, thus ultimately generating photos with enhanced perceptual quality. With comprehensive experiments, the proposed pipeline demonstrates superior performance over state-of-the-art methods as well as existing commercial tools in terms of visual quality for old photos restoration.

We propose to restore old photos that suffer from severe degradation through a deep learning approach. Unlike conventional restoration tasks that can be solved through supervised learning, the degradation in real photos is complex and the domain gap between synthetic images and real old photos makes the network fail to generalize. Therefore, we propose a novel triplet domain translation network by leveraging real photos along with massive synthetic image pairs. Specifically, we train two variational autoencoders (VAEs) to respectively transform old photos and clean photos into two latent spaces. And the translation between these two latent spaces is learned with synthetic paired data. This translation generalizes well to real photos because the domain gap is closed in the compact latent space. Besides, to address multiple degradations mixed in one old photo, we design a global branch with a partial nonlocal block targeting to the structured defects, such as scratches and dust spots, and a local branch targeting to the unstructured defects, such as noises and blurriness. Two branches are fused in the latent space, leading to improved capability to restore old photos from multiple defects. The proposed method outperforms state-of-the-art methods in terms of visual quality for old photos restoration.

Internal features from large-scale pre-trained diffusion models have recently been established as powerful semantic descriptors for a wide range of downstream tasks. Works that use these features generally need to add noise to images before passing them through the model to obtain the semantic features, as the models do not offer the most useful features when given images with little to no noise. We show that this noise has a critical impact on the usefulness of these features that cannot be remedied by ensembling with different random noises. We address this issue by introducing a lightweight, unsupervised fine-tuning method that enables diffusion backbones to provide high-quality, noise-free semantic features. We show that these features readily outperform previous diffusion features by a wide margin in a wide variety of extraction setups and downstream tasks, offering better performance than even ensemble-based methods at a fraction of the cost.

Denoising diffusion probabilistic models (DDPMs) employ a sequence of white Gaussian noise samples to generate an image. In analogy with GANs, those noise maps could be considered as the latent code associated with the generated image. However, this native noise space does not possess a convenient structure, and is thus challenging to work with in editing tasks. Here, we propose an alternative latent noise space for DDPM that enables a wide range of editing operations via simple means, and present an inversion method for extracting these edit-friendly noise maps for any given image (real or synthetically generated). As opposed to the native DDPM noise space, the edit-friendly noise maps do not have a standard normal distribution and are not statistically independent across timesteps. However, they allow perfect reconstruction of any desired image, and simple transformations on them translate into meaningful manipulations of the output image (e.g., shifting, color edits). Moreover, in text-conditional models, fixing those noise maps while changing the text prompt, modifies semantics while retaining structure. We illustrate how this property enables text-based editing of real images via the diverse DDPM sampling scheme (in contrast to the popular non-diverse DDIM inversion). We also show how it can be used within existing diffusion-based editing methods to improve their quality and diversity.

During both pretraining and fine-tuning, Large Language Models (LLMs) are trained on trillions of tokens of text of widely varying quality. Both phases of training typically involve heuristically filtering out ``low-quality'' or noisy training samples, yet little is known quantitatively about how the type or intensity of noise affects downstream performance. In this work, we study how noise in chain of thought (CoT) impacts task performance in the highly-controlled setting of algorithmically solvable tasks. First, we develop the Traced Integer (TInt) framework to generate highly customizable noised execution traces for any arithmetic function on lists of integers. We then define two types of noise: static noise, a local form of noise which is applied after the CoT trace is computed, and dynamic noise, a global form of noise which propagates errors in the trace as it is computed. We then evaluate the test performance of pretrained models both prompted and fine-tuned on noised datasets with varying levels of dataset contamination and intensity. We find fine-tuned models are extremely robust to high levels of static noise but struggle significantly more with lower levels of dynamic noise. In contrast, few-shot prompted models appear more sensitive to even static noise. We conclude with a discussion of how our findings impact noise filtering best-practices, in particular emphasizing the importance of removing samples containing destructive dynamic noise with global errors.

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect Y can be written as a function of the cause X and a noise source N independent of X, which may be scaled by a positive function g over the cause, i.e., Y = f(X) + g(X)N. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of Y given X as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

Distant and weak supervision allow to obtain large amounts of labeled training data quickly and cheaply, but these automatic annotations tend to contain a high amount of errors. A popular technique to overcome the negative effects of these noisy labels is noise modelling where the underlying noise process is modelled. In this work, we study the quality of these estimated noise models from the theoretical side by deriving the expected error of the noise model. Apart from evaluating the theoretical results on commonly used synthetic noise, we also publish NoisyNER, a new noisy label dataset from the NLP domain that was obtained through a realistic distant supervision technique. It provides seven sets of labels with differing noise patterns to evaluate different noise levels on the same instances. Parallel, clean labels are available making it possible to study scenarios where a small amount of gold-standard data can be leveraged. Our theoretical results and the corresponding experiments give insights into the factors that influence the noise model estimation like the noise distribution and the sampling technique.

We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor graph associated with the emission distribution. This allows the exponential-in-dimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is "dimension-free" in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger flow problem, where the factor graph is effectively given by the train network.

Modeling and synthesizing low-light raw noise is a fundamental problem for computational photography and image processing applications. Although most recent works have adopted physics-based models to synthesize noise, the signal-independent noise in low-light conditions is far more complicated and varies dramatically across camera sensors, which is beyond the description of these models. To address this issue, we introduce a new perspective to synthesize the signal-independent noise by a generative model. Specifically, we synthesize the signal-dependent and signal-independent noise in a physics- and learning-based manner, respectively. In this way, our method can be considered as a general model, that is, it can simultaneously learn different noise characteristics for different ISO levels and generalize to various sensors. Subsequently, we present an effective multi-scale discriminator termed Fourier transformer discriminator (FTD) to distinguish the noise distribution accurately. Additionally, we collect a new low-light raw denoising (LRD) dataset for training and benchmarking. Qualitative validation shows that the noise generated by our proposed noise model can be highly similar to the real noise in terms of distribution. Furthermore, extensive denoising experiments demonstrate that our method performs favorably against state-of-the-art methods on different sensors.

We consider the problem of computing the Walsh-Hadamard Transform (WHT) of some N-length input vector in the presence of noise, where the N-point Walsh spectrum is K-sparse with K = {O}(N^{delta}) scaling sub-linearly in the input dimension N for some 0<delta<1. Over the past decade, there has been a resurgence in research related to the computation of Discrete Fourier Transform (DFT) for some length-N input signal that has a K-sparse Fourier spectrum. In particular, through a sparse-graph code design, our earlier work on the Fast Fourier Aliasing-based Sparse Transform (FFAST) algorithm computes the K-sparse DFT in time {O}(Klog K) by taking {O}(K) noiseless samples. Inspired by the coding-theoretic design framework, Scheibler et al. proposed the Sparse Fast Hadamard Transform (SparseFHT) algorithm that elegantly computes the K-sparse WHT in the absence of noise using {O}(Klog N) samples in time {O}(Klog^2 N). However, the SparseFHT algorithm explicitly exploits the noiseless nature of the problem, and is not equipped to deal with scenarios where the observations are corrupted by noise. Therefore, a question of critical interest is whether this coding-theoretic framework can be made robust to noise. Further, if the answer is yes, what is the extra price that needs to be paid for being robust to noise? In this paper, we show, quite interestingly, that there is {\it no extra price} that needs to be paid for being robust to noise other than a constant factor. In other words, we can maintain the same sample complexity {O}(Klog N) and the computational complexity {O}(Klog^2 N) as those of the noiseless case, using our SParse Robust Iterative Graph-based Hadamard Transform (SPRIGHT) algorithm.

It is widely believed that noise conditioning is indispensable for denoising diffusion models to work successfully. This work challenges this belief. Motivated by research on blind image denoising, we investigate a variety of denoising-based generative models in the absence of noise conditioning. To our surprise, most models exhibit graceful degradation, and in some cases, they even perform better without noise conditioning. We provide a theoretical analysis of the error caused by removing noise conditioning and demonstrate that our analysis aligns with empirical observations. We further introduce a noise-unconditional model that achieves a competitive FID of 2.23 on CIFAR-10, significantly narrowing the gap to leading noise-conditional models. We hope our findings will inspire the community to revisit the foundations and formulations of denoising generative models.

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly designed dynamic Gaussian mixture distribution, which captures the dynamics of clustering structures, and is used for emitting timeseries. The generative model is parameterized by neural networks. A structured inference network is also designed for enabling inductive analysis. A gating mechanism is further introduced to dynamically tune the Gaussian mixture distributions. Extensive experimental results on a variety of real-life datasets demonstrate the effectiveness of our method.

Understanding when the noise in stochastic gradient descent (SGD) affects generalization of deep neural networks remains a challenge, complicated by the fact that networks can operate in distinct training regimes. Here we study how the magnitude of this noise T affects performance as the size of the training set P and the scale of initialization alpha are varied. For gradient descent, alpha is a key parameter that controls if the network is `lazy'(alphagg1) or instead learns features (alphall1). For classification of MNIST and CIFAR10 images, our central results are: (i) obtaining phase diagrams for performance in the (alpha,T) plane. They show that SGD noise can be detrimental or instead useful depending on the training regime. Moreover, although increasing T or decreasing alpha both allow the net to escape the lazy regime, these changes can have opposite effects on performance. (ii) Most importantly, we find that the characteristic temperature T_c where the noise of SGD starts affecting the trained model (and eventually performance) is a power law of P. We relate this finding with the observation that key dynamical quantities, such as the total variation of weights during training, depend on both T and P as power laws. These results indicate that a key effect of SGD noise occurs late in training by affecting the stopping process whereby all data are fitted. Indeed, we argue that due to SGD noise, nets must develop a stronger `signal', i.e. larger informative weights, to fit the data, leading to a longer training time. A stronger signal and a longer training time are also required when the size of the training set P increases. We confirm these views in the perceptron model, where signal and noise can be precisely measured. Interestingly, exponents characterizing the effect of SGD depend on the density of data near the decision boundary, as we explain.

The SIML (abbreviation of Separating Information Maximal Likelihood) method, has been introduced by N. Kunitomo and S. Sato and their collaborators to estimate the integrated volatility of high-frequency data that is assumed to be an It\^o process but with so-called microstructure noise. The SIML estimator turned out to share many properties with the estimator introduced by P. Malliavin and M.E. Mancino. The present paper establishes the consistency and the asymptotic normality under a general sampling scheme but without microstructure noise. Specifically, a fast convergence shown for Malliavin--Mancino estimator by E. Clement and A. Gloter is also established for the SIML estimator.

Denoising diffusion probabilistic models have been recently proposed to generate high-quality samples by estimating the gradient of the data density. The framework defines the prior noise as a standard Gaussian distribution, whereas the corresponding data distribution may be more complicated than the standard Gaussian distribution, which potentially introduces inefficiency in denoising the prior noise into the data sample because of the discrepancy between the data and the prior. In this paper, we propose PriorGrad to improve the efficiency of the conditional diffusion model for speech synthesis (for example, a vocoder using a mel-spectrogram as the condition) by applying an adaptive prior derived from the data statistics based on the conditional information. We formulate the training and sampling procedures of PriorGrad and demonstrate the advantages of an adaptive prior through a theoretical analysis. Focusing on the speech synthesis domain, we consider the recently proposed diffusion-based speech generative models based on both the spectral and time domains and show that PriorGrad achieves faster convergence and inference with superior performance, leading to an improved perceptual quality and robustness to a smaller network capacity, and thereby demonstrating the efficiency of a data-dependent adaptive prior.

Current vision systems are trained on huge datasets, and these datasets come with costs: curation is expensive, they inherit human biases, and there are concerns over privacy and usage rights. To counter these costs, interest has surged in learning from cheaper data sources, such as unlabeled images. In this paper we go a step further and ask if we can do away with real image datasets entirely, instead learning from noise processes. We investigate a suite of image generation models that produce images from simple random processes. These are then used as training data for a visual representation learner with a contrastive loss. We study two types of noise processes, statistical image models and deep generative models under different random initializations. Our findings show that it is important for the noise to capture certain structural properties of real data but that good performance can be achieved even with processes that are far from realistic. We also find that diversity is a key property to learn good representations. Datasets, models, and code are available at https://mbaradad.github.io/learning_with_noise.

N:M Structured sparsity has garnered significant interest as a result of relatively modest overhead and improved efficiency. Additionally, this form of sparsity holds considerable appeal for reducing the memory footprint owing to their modest representation overhead. There have been efforts to develop training recipes for N:M structured sparsity, they primarily focus on low-sparsity regions (sim50\%). Nonetheless, performance of models trained using these approaches tends to decline when confronted with high-sparsity regions (>80\%). In this work, we study the effectiveness of existing sparse training recipes at high-sparsity regions and argue that these methods fail to sustain the model quality on par with low-sparsity regions. We demonstrate that the significant factor contributing to this disparity is the presence of elevated levels of induced noise in the gradient magnitudes. To mitigate this undesirable effect, we employ decay mechanisms to progressively restrict the flow of gradients towards pruned elements. Our approach improves the model quality by up to 2% and 5% in vision and language models at high sparsity regime, respectively. We also evaluate the trade-off between model accuracy and training compute cost in terms of FLOPs. At iso-training FLOPs, our method yields better performance compared to conventional sparse training recipes, exhibiting an accuracy improvement of up to 2%. The source code is available at https://github.com/abhibambhaniya/progressive_gradient_flow_nm_sparsity.

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise, which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct a thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance significantly.

Large diffusion models have been successful in text-to-audio (T2A) synthesis tasks, but they often suffer from common issues such as semantic misalignment and poor temporal consistency due to limited natural language understanding and data scarcity. Additionally, 2D spatial structures widely used in T2A works lead to unsatisfactory audio quality when generating variable-length audio samples since they do not adequately prioritize temporal information. To address these challenges, we propose Make-an-Audio 2, a latent diffusion-based T2A method that builds on the success of Make-an-Audio. Our approach includes several techniques to improve semantic alignment and temporal consistency: Firstly, we use pre-trained large language models (LLMs) to parse the text into structured <event & order> pairs for better temporal information capture. We also introduce another structured-text encoder to aid in learning semantic alignment during the diffusion denoising process. To improve the performance of variable length generation and enhance the temporal information extraction, we design a feed-forward Transformer-based diffusion denoiser. Finally, we use LLMs to augment and transform a large amount of audio-label data into audio-text datasets to alleviate the problem of scarcity of temporal data. Extensive experiments show that our method outperforms baseline models in both objective and subjective metrics, and achieves significant gains in temporal information understanding, semantic consistency, and sound quality.

Recently, there has been extensive research interest in training deep networks to denoise images without clean reference. However, the representative approaches such as Noise2Noise, Noise2Void, Stein's unbiased risk estimator (SURE), etc. seem to differ from one another and it is difficult to find the coherent mathematical structure. To address this, here we present a novel approach, called Noise2Score, which reveals a missing link in order to unite these seemingly different approaches. Specifically, we show that image denoising problems without clean images can be addressed by finding the mode of the posterior distribution and that the Tweedie's formula offers an explicit solution through the score function (i.e. the gradient of log likelihood). Our method then uses the recent finding that the score function can be stably estimated from the noisy images using the amortized residual denoising autoencoder, the method of which is closely related to Noise2Noise or Nose2Void. Our Noise2Score approach is so universal that the same network training can be used to remove noises from images that are corrupted by any exponential family distributions and noise parameters. Using extensive experiments with Gaussian, Poisson, and Gamma noises, we show that Noise2Score significantly outperforms the state-of-the-art self-supervised denoising methods in the benchmark data set such as (C)BSD68, Set12, and Kodak, etc.

From whirling ceiling fans to ticking clocks, the sounds that we hear subtly vary as we move through a scene. We ask whether these ambient sounds convey information about 3D scene structure and, if so, whether they provide a useful learning signal for multimodal models. To study this, we collect a dataset of paired audio and RGB-D recordings from a variety of quiet indoor scenes. We then train models that estimate the distance to nearby walls, given only audio as input. We also use these recordings to learn multimodal representations through self-supervision, by training a network to associate images with their corresponding sounds. These results suggest that ambient sound conveys a surprising amount of information about scene structure, and that it is a useful signal for learning multimodal features.

We empirically study the effect of noise scheduling strategies for denoising diffusion generative models. There are three findings: (1) the noise scheduling is crucial for the performance, and the optimal one depends on the task (e.g., image sizes), (2) when increasing the image size, the optimal noise scheduling shifts towards a noisier one (due to increased redundancy in pixels), and (3) simply scaling the input data by a factor of b while keeping the noise schedule function fixed (equivalent to shifting the logSNR by log b) is a good strategy across image sizes. This simple recipe, when combined with recently proposed Recurrent Interface Network (RIN), yields state-of-the-art pixel-based diffusion models for high-resolution images on ImageNet, enabling single-stage, end-to-end generation of diverse and high-fidelity images at 1024times1024 resolution (without upsampling/cascades).

Low-light photography produces images with low signal-to-noise ratios due to limited photons. In such conditions, common approximations like the Gaussian noise model fall short, and many denoising techniques fail to remove noise effectively. Although deep-learning methods perform well, they require large datasets of paired images that are impractical to acquire. As a remedy, synthesizing realistic low-light noise has gained significant attention. In this paper, we investigate the ability of diffusion models to capture the complex distribution of low-light noise. We show that a naive application of conventional diffusion models is inadequate for this task and propose three key adaptations that enable high-precision noise generation without calibration or post-processing: a two-branch architecture to better model signal-dependent and signal-independent noise, the incorporation of positional information to capture fixed-pattern noise, and a tailored diffusion noise schedule. Consequently, our model enables the generation of large datasets for training low-light denoising networks, leading to state-of-the-art performance. Through comprehensive analysis, including statistical evaluation and noise decomposition, we provide deeper insights into the characteristics of the generated data.

In this work, we consider rather general and broad class of Markov chains, Ito chains, that look like Euler-Maryama discretization of some Stochastic Differential Equation. The chain we study is a unified framework for theoretical analysis. It comes with almost arbitrary isotropic and state-dependent noise instead of normal and state-independent one as in most related papers. Moreover, in our chain the drift and diffusion coefficient can be inexact in order to cover wide range of applications as Stochastic Gradient Langevin Dynamics, sampling, Stochastic Gradient Descent or Stochastic Gradient Boosting. We prove the bound in W_{2}-distance between the laws of our Ito chain and corresponding differential equation. These results improve or cover most of the known estimates. And for some particular cases, our analysis is the first.

To achieve promising results on removing noise from real-world images, most of existing denoising networks are formulated with complex network structure, making them impractical for deployment. Some attempts focused on reducing the number of filters and feature channels but suffered from large performance loss, and a more practical and lightweight denoising network with fast inference speed is of high demand. To this end, a Thumbnail based Denoising Network dubbed Thunder, is proposed and implemented as a lightweight structure for fast restoration without comprising the denoising capabilities. Specifically, the Thunder model contains two newly-established modules: (1) a wavelet-based Thumbnail Subspace Encoder (TSE) which can leverage sub-bands correlation to provide an approximate thumbnail based on the low-frequent feature; (2) a Subspace Projection based Refine Module (SPR) which can restore the details for thumbnail progressively based on the subspace projection approach. Extensive experiments have been carried out on two real-world denoising benchmarks, demonstrating that the proposed Thunder outperforms the existing lightweight models and achieves competitive performance on PSNR and SSIM when compared with the complex designs.

We present SoundStream, a novel neural audio codec that can efficiently compress speech, music and general audio at bitrates normally targeted by speech-tailored codecs. SoundStream relies on a model architecture composed by a fully convolutional encoder/decoder network and a residual vector quantizer, which are trained jointly end-to-end. Training leverages recent advances in text-to-speech and speech enhancement, which combine adversarial and reconstruction losses to allow the generation of high-quality audio content from quantized embeddings. By training with structured dropout applied to quantizer layers, a single model can operate across variable bitrates from 3kbps to 18kbps, with a negligible quality loss when compared with models trained at fixed bitrates. In addition, the model is amenable to a low latency implementation, which supports streamable inference and runs in real time on a smartphone CPU. In subjective evaluations using audio at 24kHz sampling rate, SoundStream at 3kbps outperforms Opus at 12kbps and approaches EVS at 9.6kbps. Moreover, we are able to perform joint compression and enhancement either at the encoder or at the decoder side with no additional latency, which we demonstrate through background noise suppression for speech.

Optical coherence tomography (OCT) imaging from different camera devices causes challenging domain shifts and can cause a severe drop in accuracy for machine learning models. In this work, we introduce a minimal noise adaptation method based on a singular value decomposition (SVDNA) to overcome the domain gap between target domains from three different device manufacturers in retinal OCT imaging. Our method utilizes the difference in noise structure to successfully bridge the domain gap between different OCT devices and transfer the style from unlabeled target domain images to source images for which manual annotations are available. We demonstrate how this method, despite its simplicity, compares or even outperforms state-of-the-art unsupervised domain adaptation methods for semantic segmentation on a public OCT dataset. SVDNA can be integrated with just a few lines of code into the augmentation pipeline of any network which is in contrast to many state-of-the-art domain adaptation methods which often need to change the underlying model architecture or train a separate style transfer model. The full code implementation for SVDNA is available at https://github.com/ValentinKoch/SVDNA.

Enhancing the visibility in extreme low-light environments is a challenging task. Under nearly lightless condition, existing image denoising methods could easily break down due to significantly low SNR. In this paper, we systematically study the noise statistics in the imaging pipeline of CMOS photosensors, and formulate a comprehensive noise model that can accurately characterize the real noise structures. Our novel model considers the noise sources caused by digital camera electronics which are largely overlooked by existing methods yet have significant influence on raw measurement in the dark. It provides a way to decouple the intricate noise structure into different statistical distributions with physical interpretations. Moreover, our noise model can be used to synthesize realistic training data for learning-based low-light denoising algorithms. In this regard, although promising results have been shown recently with deep convolutional neural networks, the success heavily depends on abundant noisy clean image pairs for training, which are tremendously difficult to obtain in practice. Generalizing their trained models to images from new devices is also problematic. Extensive experiments on multiple low-light denoising datasets -- including a newly collected one in this work covering various devices -- show that a deep neural network trained with our proposed noise formation model can reach surprisingly-high accuracy. The results are on par with or sometimes even outperform training with paired real data, opening a new door to real-world extreme low-light photography.

State-space models (SSMs) have recently emerged as a framework for learning long-range sequence tasks. An example is the structured state-space sequence (S4) layer, which uses the diagonal-plus-low-rank structure of the HiPPO initialization framework. However, the complicated structure of the S4 layer poses challenges; and, in an effort to address these challenges, models such as S4D and S5 have considered a purely diagonal structure. This choice simplifies the implementation, improves computational efficiency, and allows channel communication. However, diagonalizing the HiPPO framework is itself an ill-posed problem. In this paper, we propose a general solution for this and related ill-posed diagonalization problems in machine learning. We introduce a generic, backward-stable "perturb-then-diagonalize" (PTD) methodology, which is based on the pseudospectral theory of non-normal operators, and which may be interpreted as the approximate diagonalization of the non-normal matrices defining SSMs. Based on this, we introduce the S4-PTD and S5-PTD models. Through theoretical analysis of the transfer functions of different initialization schemes, we demonstrate that the S4-PTD/S5-PTD initialization strongly converges to the HiPPO framework, while the S4D/S5 initialization only achieves weak convergences. As a result, our new models show resilience to Fourier-mode noise-perturbed inputs, a crucial property not achieved by the S4D/S5 models. In addition to improved robustness, our S5-PTD model averages 87.6% accuracy on the Long-Range Arena benchmark, demonstrating that the PTD methodology helps to improve the accuracy of deep learning models.

We study the problem of online generalized linear regression in the stochastic setting, where the label is generated from a generalized linear model with possibly unbounded additive noise. We provide a sharp analysis of the classical follow-the-regularized-leader (FTRL) algorithm to cope with the label noise. More specifically, for sigma-sub-Gaussian label noise, our analysis provides a regret upper bound of O(sigma^2 d log T) + o(log T), where d is the dimension of the input vector, T is the total number of rounds. We also prove a Omega(sigma^2dlog(T/d)) lower bound for stochastic online linear regression, which indicates that our upper bound is nearly optimal. In addition, we extend our analysis to a more refined Bernstein noise condition. As an application, we study generalized linear bandits with heteroscedastic noise and propose an algorithm based on FTRL to achieve the first variance-aware regret bound.

Recently, the mainstream practice for training low-light raw image denoising methods has shifted towards employing synthetic data. Noise modeling, which focuses on characterizing the noise distribution of real-world sensors, profoundly influences the effectiveness and practicality of synthetic data. Currently, physics-based noise modeling struggles to characterize the entire real noise distribution, while learning-based noise modeling impractically depends on paired real data. In this paper, we propose a novel strategy: learning the noise model from dark frames instead of paired real data, to break down the data dependency. Based on this strategy, we introduce an efficient physics-guided noise neural proxy (PNNP) to approximate the real-world sensor noise model. Specifically, we integrate physical priors into neural proxies and introduce three efficient techniques: physics-guided noise decoupling (PND), physics-guided proxy model (PPM), and differentiable distribution loss (DDL). PND decouples the dark frame into different components and handles different levels of noise flexibly, which reduces the complexity of noise modeling. PPM incorporates physical priors to constrain the generated noise, which promotes the accuracy of noise modeling. DDL provides explicit and reliable supervision for noise distribution, which promotes the precision of noise modeling. PNNP exhibits powerful potential in characterizing the real noise distribution. Extensive experiments on public datasets demonstrate superior performance in practical low-light raw image denoising. The code will be available at https://github.com/fenghansen/PNNP.

The brain is a noisy system subject to energy constraints. These facts are rarely taken into account when modelling artificial neural networks. In this paper, we are interested in demonstrating that those factors can actually lead to the appearance of robust associative memories. We first propose a simplified model of noise in the brain, taking into account synaptic noise and interference from neurons external to the network. When coarsely quantized, we show that this noise can be reduced to insertions and erasures. We take a neural network with recurrent modifiable connections, and subject it to noisy external inputs. We introduce an energy usage limitation principle in the network as well as consolidated Hebbian learning, resulting in an incremental processing of inputs. We show that the connections naturally formed correspond to state-of-the-art binary sparse associative memories.

In this work, we build upon our previous publication and use diffusion-based generative models for speech enhancement. We present a detailed overview of the diffusion process that is based on a stochastic differential equation and delve into an extensive theoretical examination of its implications. Opposed to usual conditional generation tasks, we do not start the reverse process from pure Gaussian noise but from a mixture of noisy speech and Gaussian noise. This matches our forward process which moves from clean speech to noisy speech by including a drift term. We show that this procedure enables using only 30 diffusion steps to generate high-quality clean speech estimates. By adapting the network architecture, we are able to significantly improve the speech enhancement performance, indicating that the network, rather than the formalism, was the main limitation of our original approach. In an extensive cross-dataset evaluation, we show that the improved method can compete with recent discriminative models and achieves better generalization when evaluating on a different corpus than used for training. We complement the results with an instrumental evaluation using real-world noisy recordings and a listening experiment, in which our proposed method is rated best. Examining different sampler configurations for solving the reverse process allows us to balance the performance and computational speed of the proposed method. Moreover, we show that the proposed method is also suitable for dereverberation and thus not limited to additive background noise removal. Code and audio examples are available online, see https://github.com/sp-uhh/sgmse

Diffusion models have opened the path to a wide range of text-based image editing frameworks. However, these typically build on the multi-step nature of the diffusion backwards process, and adapting them to distilled, fast-sampling methods has proven surprisingly challenging. Here, we focus on a popular line of text-based editing frameworks - the ``edit-friendly'' DDPM-noise inversion approach. We analyze its application to fast sampling methods and categorize its failures into two classes: the appearance of visual artifacts, and insufficient editing strength. We trace the artifacts to mismatched noise statistics between inverted noises and the expected noise schedule, and suggest a shifted noise schedule which corrects for this offset. To increase editing strength, we propose a pseudo-guidance approach that efficiently increases the magnitude of edits without introducing new artifacts. All in all, our method enables text-based image editing with as few as three diffusion steps, while providing novel insights into the mechanisms behind popular text-based editing approaches.

We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding of graduate-level concepts such as Langevin dynamics or score matching appears to be required to grasp how it works. We propose an alternative approach that requires no more than undergrad calculus and probability. We consider two densities and observe what happens when random samples from these densities are blended (linearly interpolated). We show that iteratively blending and deblending samples produces random paths between the two densities that converge toward a deterministic mapping. This mapping can be evaluated with a neural network trained to deblend samples. We obtain a model that behaves like deterministic denoising diffusion: it iteratively maps samples from one density (e.g., Gaussian noise) to another (e.g., cat images). However, compared to the state-of-the-art alternative, our model is simpler to derive, simpler to implement, more numerically stable, achieves higher quality results in our experiments, and has interesting connections to computer graphics.

When training neural networks, it has been widely observed that a large step size is essential in stochastic gradient descent (SGD) for obtaining superior models. However, the effect of large step sizes on the success of SGD is not well understood theoretically. Several previous works have attributed this success to the stochastic noise present in SGD. However, we show through a novel set of experiments that the stochastic noise is not sufficient to explain good non-convex training, and that instead the effect of a large learning rate itself is essential for obtaining best performance.We demonstrate the same effects also in the noise-less case, i.e. for full-batch GD. We formally prove that GD with large step size -- on certain non-convex function classes -- follows a different trajectory than GD with a small step size, which can lead to convergence to a global minimum instead of a local one. Our settings provide a framework for future analysis which allows comparing algorithms based on behaviors that can not be observed in the traditional settings.

Diffusion models excel in generating high-quality images. However, current diffusion models struggle to produce reliable images without guidance methods, such as classifier-free guidance (CFG). Are guidance methods truly necessary? Observing that noise obtained via diffusion inversion can reconstruct high-quality images without guidance, we focus on the initial noise of the denoising pipeline. By mapping Gaussian noise to `guidance-free noise', we uncover that small low-magnitude low-frequency components significantly enhance the denoising process, removing the need for guidance and thus improving both inference throughput and memory. Expanding on this, we propose \ours, a novel method that replaces guidance methods with a single refinement of the initial noise. This refined noise enables high-quality image generation without guidance, within the same diffusion pipeline. Our noise-refining model leverages efficient noise-space learning, achieving rapid convergence and strong performance with just 50K text-image pairs. We validate its effectiveness across diverse metrics and analyze how refined noise can eliminate the need for guidance. See our project page: https://cvlab-kaist.github.io/NoiseRefine/.

In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size n is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in R^K, where samples are assumed to be corrupted by a multi-variate additive Gaussian noise of an arbitrary magnitude. We prove the existence of an algorithm that with high probability outputs a simplex having a ell_2 distance of at most varepsilon from the true simplex (for any varepsilon>0). Also, we theoretically show that in order to achieve this bound, it is sufficient to have ngeleft(K^2/varepsilon^2right)e^{Omegaleft(K/SNR^2right)} samples, where SNR stands for the signal-to-noise ratio. This result solves an important open problem and shows as long as SNRgeOmegaleft(K^{1/2}right), the sample complexity of the noisy regime has the same order to that of the noiseless case. Our proofs are a combination of the so-called sample compression technique in ashtiani2018nearly, mathematical tools from high-dimensional geometry, and Fourier analysis. In particular, we have proposed a general Fourier-based technique for recovery of a more general class of distribution families from additive Gaussian noise, which can be further used in a variety of other related problems.

Diffusion models have emerged as the de facto choice for generating visual signals. However, training a single model to predict noise across various levels poses significant challenges, necessitating numerous iterations and incurring significant computational costs. Various approaches, such as loss weighting strategy design and architectural refinements, have been introduced to expedite convergence. In this study, we propose a novel approach to design the noise schedule for enhancing the training of diffusion models. Our key insight is that the importance sampling of the logarithm of the Signal-to-Noise ratio (logSNR), theoretically equivalent to a modified noise schedule, is particularly beneficial for training efficiency when increasing the sample frequency around log SNR=0. We empirically demonstrate the superiority of our noise schedule over the standard cosine schedule. Furthermore, we highlight the advantages of our noise schedule design on the ImageNet benchmark, showing that the designed schedule consistently benefits different prediction targets.

We introduce a novel, general-purpose audio generation framework specifically designed for anomaly detection and localization. Unlike existing datasets that predominantly focus on industrial and machine-related sounds, our framework focuses a broader range of environments, particularly useful in real-world scenarios where only audio data are available, such as in video-derived or telephonic audio. To generate such data, we propose a new method inspired by the LLM-Modulo framework, which leverages large language models(LLMs) as world models to simulate such real-world scenarios. This tool is modular allowing a plug-and-play approach. It operates by first using LLMs to predict plausible real-world scenarios. An LLM further extracts the constituent sounds, the order and the way in which these should be merged to create coherent wholes. Much like the LLM-Modulo framework, we include rigorous verification of each output stage, ensuring the reliability of the generated data. The data produced using the framework serves as a benchmark for anomaly detection applications, potentially enhancing the performance of models trained on audio data, particularly in handling out-of-distribution cases. Our contributions thus fill a critical void in audio anomaly detection resources and provide a scalable tool for generating diverse, realistic audio data.

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

In text-to-speech (TTS) synthesis, diffusion models have achieved promising generation quality. However, because of the pre-defined data-to-noise diffusion process, their prior distribution is restricted to a noisy representation, which provides little information of the generation target. In this work, we present a novel TTS system, Bridge-TTS, making the first attempt to substitute the noisy Gaussian prior in established diffusion-based TTS methods with a clean and deterministic one, which provides strong structural information of the target. Specifically, we leverage the latent representation obtained from text input as our prior, and build a fully tractable Schrodinger bridge between it and the ground-truth mel-spectrogram, leading to a data-to-data process. Moreover, the tractability and flexibility of our formulation allow us to empirically study the design spaces such as noise schedules, as well as to develop stochastic and deterministic samplers. Experimental results on the LJ-Speech dataset illustrate the effectiveness of our method in terms of both synthesis quality and sampling efficiency, significantly outperforming our diffusion counterpart Grad-TTS in 50-step/1000-step synthesis and strong fast TTS models in few-step scenarios. Project page: https://bridge-tts.github.io/

This paper tackles the problem of the heavy dependence of clean speech data required by deep learning based audio-denoising methods by showing that it is possible to train deep speech denoising networks using only noisy speech samples. Conventional wisdom dictates that in order to achieve good speech denoising performance, there is a requirement for a large quantity of both noisy speech samples and perfectly clean speech samples, resulting in a need for expensive audio recording equipment and extremely controlled soundproof recording studios. These requirements pose significant challenges in data collection, especially in economically disadvantaged regions and for low resource languages. This work shows that speech denoising deep neural networks can be successfully trained utilizing only noisy training audio. Furthermore it is revealed that such training regimes achieve superior denoising performance over conventional training regimes utilizing clean training audio targets, in cases involving complex noise distributions and low Signal-to-Noise ratios (high noise environments). This is demonstrated through experiments studying the efficacy of our proposed approach over both real-world noises and synthetic noises using the 20 layered Deep Complex U-Net architecture.

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical understanding of their observed properties is still lacking, in particular, their weak sensitivity to the choice of noise family and the role of adequate scheduling of noise levels for good synthesis. By identifying a correspondence between diffusion models and a well-known paradigm in cognitive science known as serial reproduction, whereby human agents iteratively observe and reproduce stimuli from memory, we show how the aforementioned properties of diffusion models can be explained as a natural consequence of this correspondence. We then complement our theoretical analysis with simulations that exhibit these key features. Our work highlights how classic paradigms in cognitive science can shed light on state-of-the-art machine learning problems.

Diffusion-based image super-resolution methods have demonstrated significant advantages over GAN-based approaches, particularly in terms of perceptual quality. Building upon a lengthy Markov chain, diffusion-based methods possess remarkable modeling capacity, enabling them to achieve outstanding performance in real-world scenarios. Unlike previous methods that focus on modifying the noise schedule or sampling process to enhance performance, our approach emphasizes the improved utilization of LR information. We find that different regions of the LR image can be viewed as corresponding to different timesteps in a diffusion process, where flat areas are closer to the target HR distribution but edge and texture regions are farther away. In these flat areas, applying a slight noise is more advantageous for the reconstruction. We associate this characteristic with uncertainty and propose to apply uncertainty estimate to guide region-specific noise level control, a technique we refer to as Uncertainty-guided Noise Weighting. Pixels with lower uncertainty (i.e., flat regions) receive reduced noise to preserve more LR information, therefore improving performance. Furthermore, we modify the network architecture of previous methods to develop our Uncertainty-guided Perturbation Super-Resolution (UPSR) model. Extensive experimental results demonstrate that, despite reduced model size and training overhead, the proposed UWSR method outperforms current state-of-the-art methods across various datasets, both quantitatively and qualitatively.

Poisson noise suppression is an important preprocessing step in several applications, such as medical imaging, microscopy, and astronomical imaging. In this work, we propose a novel patch-wise Poisson noise removal strategy, in which the MMSE estimator is utilized in order to produce the denoising result for each image patch. Fast and accurate computation of the MMSE estimator is carried out using k-d tree search followed by search in the K-nearest neighbor graph. Our experiments show that the proposed method is the preferable choice for low signal-to-noise ratios.

Image interpolation based on diffusion models is promising in creating fresh and interesting images. Advanced interpolation methods mainly focus on spherical linear interpolation, where images are encoded into the noise space and then interpolated for denoising to images. However, existing methods face challenges in effectively interpolating natural images (not generated by diffusion models), thereby restricting their practical applicability. Our experimental investigations reveal that these challenges stem from the invalidity of the encoding noise, which may no longer obey the expected noise distribution, e.g., a normal distribution. To address these challenges, we propose a novel approach to correct noise for image interpolation, NoiseDiffusion. Specifically, NoiseDiffusion approaches the invalid noise to the expected distribution by introducing subtle Gaussian noise and introduces a constraint to suppress noise with extreme values. In this context, promoting noise validity contributes to mitigating image artifacts, but the constraint and introduced exogenous noise typically lead to a reduction in signal-to-noise ratio, i.e., loss of original image information. Hence, NoiseDiffusion performs interpolation within the noisy image space and injects raw images into these noisy counterparts to address the challenge of information loss. Consequently, NoiseDiffusion enables us to interpolate natural images without causing artifacts or information loss, thus achieving the best interpolation results.

We introduce Noise2Music, where a series of diffusion models is trained to generate high-quality 30-second music clips from text prompts. Two types of diffusion models, a generator model, which generates an intermediate representation conditioned on text, and a cascader model, which generates high-fidelity audio conditioned on the intermediate representation and possibly the text, are trained and utilized in succession to generate high-fidelity music. We explore two options for the intermediate representation, one using a spectrogram and the other using audio with lower fidelity. We find that the generated audio is not only able to faithfully reflect key elements of the text prompt such as genre, tempo, instruments, mood, and era, but goes beyond to ground fine-grained semantics of the prompt. Pretrained large language models play a key role in this story -- they are used to generate paired text for the audio of the training set and to extract embeddings of the text prompts ingested by the diffusion models. Generated examples: https://google-research.github.io/noise2music

Text-to-image diffusion model is a popular paradigm that synthesizes personalized images by providing a text prompt and a random Gaussian noise. While people observe that some noises are ``golden noises'' that can achieve better text-image alignment and higher human preference than others, we still lack a machine learning framework to obtain those golden noises. To learn golden noises for diffusion sampling, we mainly make three contributions in this paper. First, we identify a new concept termed the noise prompt, which aims at turning a random Gaussian noise into a golden noise by adding a small desirable perturbation derived from the text prompt. Following the concept, we first formulate the noise prompt learning framework that systematically learns ``prompted'' golden noise associated with a text prompt for diffusion models. Second, we design a noise prompt data collection pipeline and collect a large-scale noise prompt dataset~(NPD) that contains 100k pairs of random noises and golden noises with the associated text prompts. With the prepared NPD as the training dataset, we trained a small noise prompt network~(NPNet) that can directly learn to transform a random noise into a golden noise. The learned golden noise perturbation can be considered as a kind of prompt for noise, as it is rich in semantic information and tailored to the given text prompt. Third, our extensive experiments demonstrate the impressive effectiveness and generalization of NPNet on improving the quality of synthesized images across various diffusion models, including SDXL, DreamShaper-xl-v2-turbo, and Hunyuan-DiT. Moreover, NPNet is a small and efficient controller that acts as a plug-and-play module with very limited additional inference and computational costs, as it just provides a golden noise instead of a random noise without accessing the original pipeline.

Classifier-Free Guidance (CFG) is a fundamental technique in training conditional diffusion models. The common practice for CFG-based training is to use a single network to learn both conditional and unconditional noise prediction, with a small dropout rate for conditioning. However, we observe that the joint learning of unconditional noise with limited bandwidth in training results in poor priors for the unconditional case. More importantly, these poor unconditional noise predictions become a serious reason for degrading the quality of conditional generation. Inspired by the fact that most CFG-based conditional models are trained by fine-tuning a base model with better unconditional generation, we first show that simply replacing the unconditional noise in CFG with that predicted by the base model can significantly improve conditional generation. Furthermore, we show that a diffusion model other than the one the fine-tuned model was trained on can be used for unconditional noise replacement. We experimentally verify our claim with a range of CFG-based conditional models for both image and video generation, including Zero-1-to-3, Versatile Diffusion, DiT, DynamiCrafter, and InstructPix2Pix.

Score-based generative models (SGMs) have recently shown impressive results for difficult generative tasks such as the unconditional and conditional generation of natural images and audio signals. In this work, we extend these models to the complex short-time Fourier transform (STFT) domain, proposing a novel training task for speech enhancement using a complex-valued deep neural network. We derive this training task within the formalism of stochastic differential equations (SDEs), thereby enabling the use of predictor-corrector samplers. We provide alternative formulations inspired by previous publications on using generative diffusion models for speech enhancement, avoiding the need for any prior assumptions on the noise distribution and making the training task purely generative which, as we show, results in improved enhancement performance.

In this article, we study the consistency of the template estimation with the Fr\'echet mean in quotient spaces. The Fr\'echet mean in quotient spaces is often used when the observations are deformed or transformed by a group action. We show that in most cases this estimator is actually inconsistent. We exhibit a sufficient condition for this inconsistency, which amounts to the folding of the distribution of the noisy template when it is projected to the quotient space. This condition appears to be fulfilled as soon as the support of the noise is large enough. To quantify this inconsistency we provide lower and upper bounds of the bias as a function of the variability (the noise level). This shows that the consistency bias cannot be neglected when the variability increases.

We study the estimation of a planted signal hidden in a recently introduced nested matrix-tensor model, which is an extension of the classical spiked rank-one tensor model, motivated by multi-view clustering. Prior work has theoretically examined the performance of a tensor-based approach, which relies on finding a best rank-one approximation, a problem known to be computationally hard. A tractable alternative approach consists in computing instead the best rank-one (matrix) approximation of an unfolding of the observed tensor data, but its performance was hitherto unknown. We quantify here the performance gap between these two approaches, in particular by deriving the precise algorithmic threshold of the unfolding approach and demonstrating that it exhibits a BBP-type transition behavior. This work is therefore in line with recent contributions which deepen our understanding of why tensor-based methods surpass matrix-based methods in handling structured tensor data.

We present a state-of-the-art speech recognition system developed using end-to-end deep learning. Our architecture is significantly simpler than traditional speech systems, which rely on laboriously engineered processing pipelines; these traditional systems also tend to perform poorly when used in noisy environments. In contrast, our system does not need hand-designed components to model background noise, reverberation, or speaker variation, but instead directly learns a function that is robust to such effects. We do not need a phoneme dictionary, nor even the concept of a "phoneme." Key to our approach is a well-optimized RNN training system that uses multiple GPUs, as well as a set of novel data synthesis techniques that allow us to efficiently obtain a large amount of varied data for training. Our system, called Deep Speech, outperforms previously published results on the widely studied Switchboard Hub5'00, achieving 16.0% error on the full test set. Deep Speech also handles challenging noisy environments better than widely used, state-of-the-art commercial speech systems.

We discover that common diffusion noise schedules do not enforce the last timestep to have zero signal-to-noise ratio (SNR), and some implementations of diffusion samplers do not start from the last timestep. Such designs are flawed and do not reflect the fact that the model is given pure Gaussian noise at inference, creating a discrepancy between training and inference. We show that the flawed design causes real problems in existing implementations. In Stable Diffusion, it severely limits the model to only generate images with medium brightness and prevents it from generating very bright and dark samples. We propose a few simple fixes: (1) rescale the noise schedule to enforce zero terminal SNR; (2) train the model with v prediction; (3) change the sampler to always start from the last timestep; (4) rescale classifier-free guidance to prevent over-exposure. These simple changes ensure the diffusion process is congruent between training and inference and allow the model to generate samples more faithful to the original data distribution.

It is well known that many open-released foundational diffusion models have difficulty in generating images that substantially depart from average brightness, despite such images being present in the training data. This is due to an inconsistency: while denoising starts from pure Gaussian noise during inference, the training noise schedule retains residual data even in the final timestep distribution, due to difficulties in numerical conditioning in mainstream formulation, leading to unintended bias during inference. To mitigate this issue, certain epsilon-prediction models are combined with an ad-hoc offset-noise methodology. In parallel, some contemporary models have adopted zero-terminal SNR noise schedules together with v-prediction, which necessitate major alterations to pre-trained models. However, such changes risk destabilizing a large multitude of community-driven applications anchored on these pre-trained models. In light of this, our investigation revisits the fundamental causes, leading to our proposal of an innovative and principled remedy, called One More Step (OMS). By integrating a compact network and incorporating an additional simple yet effective step during inference, OMS elevates image fidelity and harmonizes the dichotomy between training and inference, while preserving original model parameters. Once trained, various pre-trained diffusion models with the same latent domain can share the same OMS module.

Spectrograms are 2D representations of sound that look very different from the images found in our visual world. And natural images, when played as spectrograms, make unnatural sounds. In this paper, we show that it is possible to synthesize spectrograms that simultaneously look like natural images and sound like natural audio. We call these spectrograms images that sound. Our approach is simple and zero-shot, and it leverages pre-trained text-to-image and text-to-spectrogram diffusion models that operate in a shared latent space. During the reverse process, we denoise noisy latents with both the audio and image diffusion models in parallel, resulting in a sample that is likely under both models. Through quantitative evaluations and perceptual studies, we find that our method successfully generates spectrograms that align with a desired audio prompt while also taking the visual appearance of a desired image prompt. Please see our project page for video results: https://ificl.github.io/images-that-sound/

Learning signed distance functions (SDFs) from 3D point clouds is an important task in 3D computer vision. However, without ground truth signed distances, point normals or clean point clouds, current methods still struggle from learning SDFs from noisy point clouds. To overcome this challenge, we propose to learn SDFs via a noise to noise mapping, which does not require any clean point cloud or ground truth supervision for training. Our novelty lies in the noise to noise mapping which can infer a highly accurate SDF of a single object or scene from its multiple or even single noisy point cloud observations. Our novel learning manner is supported by modern Lidar systems which capture multiple noisy observations per second. We achieve this by a novel loss which enables statistical reasoning on point clouds and maintains geometric consistency although point clouds are irregular, unordered and have no point correspondence among noisy observations. Our evaluation under the widely used benchmarks demonstrates our superiority over the state-of-the-art methods in surface reconstruction, point cloud denoising and upsampling. Our code, data, and pre-trained models are available at https://github.com/mabaorui/Noise2NoiseMapping/

We propose the Signal Dice Similarity Coefficient (SDSC), a structure-aware metric function for time series self-supervised representation learning. Most Self-Supervised Learning (SSL) methods for signals commonly adopt distance-based objectives such as mean squared error (MSE), which are sensitive to amplitude, invariant to waveform polarity, and unbounded in scale. These properties hinder semantic alignment and reduce interpretability. SDSC addresses this by quantifying structural agreement between temporal signals based on the intersection of signed amplitudes, derived from the Dice Similarity Coefficient (DSC).Although SDSC is defined as a structure-aware metric, it can be used as a loss by subtracting from 1 and applying a differentiable approximation of the Heaviside function for gradient-based optimization. A hybrid loss formulation is also proposed to combine SDSC with MSE, improving stability and preserving amplitude where necessary. Experiments on forecasting and classification benchmarks demonstrate that SDSC-based pre-training achieves comparable or improved performance over MSE, particularly in in-domain and low-resource scenarios. The results suggest that structural fidelity in signal representations enhances the semantic representation quality, supporting the consideration of structure-aware metrics as viable alternatives to conventional distance-based methods.

Conditional diffusion models have shown remarkable performance in various generative tasks, but training them requires large-scale datasets that often contain noise in conditional inputs, a.k.a. noisy labels. This noise leads to condition mismatch and quality degradation of generated data. This paper proposes Transition-aware weighted Denoising Score Matching (TDSM) for training conditional diffusion models with noisy labels, which is the first study in the line of diffusion models. The TDSM objective contains a weighted sum of score networks, incorporating instance-wise and time-dependent label transition probabilities. We introduce a transition-aware weight estimator, which leverages a time-dependent noisy-label classifier distinctively customized to the diffusion process. Through experiments across various datasets and noisy label settings, TDSM improves the quality of generated samples aligned with given conditions. Furthermore, our method improves generation performance even on prevalent benchmark datasets, which implies the potential noisy labels and their risk of generative model learning. Finally, we show the improved performance of TDSM on top of conventional noisy label corrections, which empirically proving its contribution as a part of label-noise robust generative models. Our code is available at: https://github.com/byeonghu-na/tdsm.

Given a factorization of an image into a sum of linear components, we present a zero-shot method to control each individual component through diffusion model sampling. For example, we can decompose an image into low and high spatial frequencies and condition these components on different text prompts. This produces hybrid images, which change appearance depending on viewing distance. By decomposing an image into three frequency subbands, we can generate hybrid images with three prompts. We also use a decomposition into grayscale and color components to produce images whose appearance changes when they are viewed in grayscale, a phenomena that naturally occurs under dim lighting. And we explore a decomposition by a motion blur kernel, which produces images that change appearance under motion blurring. Our method works by denoising with a composite noise estimate, built from the components of noise estimates conditioned on different prompts. We also show that for certain decompositions, our method recovers prior approaches to compositional generation and spatial control. Finally, we show that we can extend our approach to generate hybrid images from real images. We do this by holding one component fixed and generating the remaining components, effectively solving an inverse problem.

Pre-training on large-scale datasets and then fine-tuning on downstream tasks have become a standard practice in deep learning. However, pre-training data often contain label noise that may adversely affect the generalization of the model. This paper aims to understand the nature of noise in pre-training datasets and to mitigate its impact on downstream tasks. More specifically, through extensive experiments of supervised pre-training models on synthetic noisy ImageNet-1K and YFCC15M datasets, we demonstrate that while slight noise in pre-training can benefit in-domain (ID) transfer performance, where the training and testing data share the same distribution, it always deteriorates out-of-domain (OOD) performance, where training and testing data distribution are different. We empirically verify that the reason behind is noise in pre-training shapes the feature space differently. We then propose a light-weight black-box tuning method (NMTune) to affine the feature space to mitigate the malignant effect of noise and improve generalization on both ID and OOD tasks, considering one may not be able to fully fine-tune or even access the pre-trained models. We conduct practical experiments on popular vision and language models that are pre-trained on noisy data for evaluation of our approach. Our analysis and results show the importance of this interesting and novel research direction, which we term Noisy Model Learning.

We study the sparse recovery problem with an underdetermined linear system characterized by a Kronecker-structured dictionary and a Kronecker-supported sparse vector. We cast this problem into the sparse Bayesian learning (SBL) framework and rely on the expectation-maximization method for a solution. To this end, we model the Kronecker-structured support with a hierarchical Gaussian prior distribution parameterized by a Kronecker-structured hyperparameter, leading to a non-convex optimization problem. The optimization problem is solved using the alternating minimization (AM) method and a singular value decomposition (SVD)-based method, resulting in two algorithms. Further, we analytically guarantee that the AM-based method converges to the stationary point of the SBL cost function. The SVD-based method, though it adopts approximations, is empirically shown to be more efficient and accurate. We then apply our algorithm to estimate the uplink wireless channel in an intelligent reflecting surface-aided MIMO system and extend the AM-based algorithm to address block sparsity in the channel. We also study the SBL cost to show that the minima of the cost function are achieved at sparse solutions and that incorporating the Kronecker structure reduces the number of local minima of the SBL cost function. Our numerical results demonstrate the effectiveness of our algorithms compared to the state-of-the-art.

Denoising diffusion models have recently shown impressive results in generative tasks. By learning powerful priors from huge collections of training images, such models are able to gradually modify complete noise to a clean natural image via a sequence of small denoising steps, seemingly making them well-suited for single image denoising. However, effectively applying denoising diffusion models to removal of realistic noise is more challenging than it may seem, since their formulation is based on additive white Gaussian noise, unlike noise in real-world images. In this work, we present SVNR, a novel formulation of denoising diffusion that assumes a more realistic, spatially-variant noise model. SVNR enables using the noisy input image as the starting point for the denoising diffusion process, in addition to conditioning the process on it. To this end, we adapt the diffusion process to allow each pixel to have its own time embedding, and propose training and inference schemes that support spatially-varying time maps. Our formulation also accounts for the correlation that exists between the condition image and the samples along the modified diffusion process. In our experiments we demonstrate the advantages of our approach over a strong diffusion model baseline, as well as over a state-of-the-art single image denoising method.

Recently, denoising diffusion probabilistic models and generative score matching have shown high potential in modelling complex data distributions while stochastic calculus has provided a unified point of view on these techniques allowing for flexible inference schemes. In this paper we introduce Grad-TTS, a novel text-to-speech model with score-based decoder producing mel-spectrograms by gradually transforming noise predicted by encoder and aligned with text input by means of Monotonic Alignment Search. The framework of stochastic differential equations helps us to generalize conventional diffusion probabilistic models to the case of reconstructing data from noise with different parameters and allows to make this reconstruction flexible by explicitly controlling trade-off between sound quality and inference speed. Subjective human evaluation shows that Grad-TTS is competitive with state-of-the-art text-to-speech approaches in terms of Mean Opinion Score. We will make the code publicly available shortly.

Calibration-based methods have dominated RAW image denoising under extremely low-light environments. However, these methods suffer from several main deficiencies: 1) the calibration procedure is laborious and time-consuming, 2) denoisers for different cameras are difficult to transfer, and 3) the discrepancy between synthetic noise and real noise is enlarged by high digital gain. To overcome the above shortcomings, we propose a calibration-free pipeline for Lighting Every Drakness (LED), regardless of the digital gain or camera sensor. Instead of calibrating the noise parameters and training repeatedly, our method could adapt to a target camera only with few-shot paired data and fine-tuning. In addition, well-designed structural modification during both stages alleviates the domain gap between synthetic and real noise without any extra computational cost. With 2 pairs for each additional digital gain (in total 6 pairs) and 0.5% iterations, our method achieves superior performance over other calibration-based methods. Our code is available at https://github.com/Srameo/LED .

Robustness is essential for deep neural networks, especially in security-sensitive applications. To this end, randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations. Recently, diffusion models have been successfully employed for randomized smoothing to purify noise-perturbed samples before making predictions with a standard classifier. While these methods excel at small perturbation radii, they struggle with larger perturbations and incur a significant computational overhead during inference compared to classical methods. To address this, we reformulate the generative modeling task along the diffusion trajectories in pixel space as a discriminative task in the latent space. Specifically, we use instance discrimination to achieve consistent representations along the trajectories by aligning temporally adjacent points. After fine-tuning based on the learned representations, our model enables implicit denoising-then-classification via a single prediction, substantially reducing inference costs. We conduct extensive experiments on various datasets and achieve state-of-the-art performance with minimal computation budget during inference. For example, our method outperforms the certified accuracy of diffusion-based methods on ImageNet across all perturbation radii by 5.3% on average, with up to 11.6% at larger radii, while reducing inference costs by 85times on average. Codes are available at: https://github.com/jiachenlei/rRCM.

This article investigates signal estimation in wireless transmission (i.e., receive beamforming) from the perspective of statistical machine learning, where the transmit signals may be from an integrated sensing and communication system; that is, 1) signals may be not only discrete constellation points but also arbitrary complex values; 2) signals may be spatially correlated. Particular attention is paid to handling various uncertainties such as the uncertainty of the transmit signal covariance, the uncertainty of the channel matrix, the uncertainty of the channel noise covariance, the existence of channel impulse noises, and the limited sample size of pilots. To proceed, a distributionally robust machine learning framework that is insensitive to the above uncertainties is proposed, which reveals that channel estimation is not a necessary operation. For optimal linear estimation, the proposed framework includes several existing beamformers as special cases such as diagonal loading and eigenvalue thresholding. For optimal nonlinear estimation, estimators are limited in reproducing kernel Hilbert spaces and neural network function spaces, and corresponding uncertainty-aware solutions (e.g., kernelized diagonal loading) are derived. In addition, we prove that the ridge and kernel ridge regression methods in machine learning are distributionally robust against diagonal perturbation in feature covariance.

Sparsity in the structure of Neural Networks can lead to less energy consumption, less memory usage, faster computation times on convenient hardware, and automated machine learning. If sparsity gives rise to certain kinds of structure, it can explain automatically obtained features during learning. We provide insights into experiments in which we show how sparsity can be achieved through prior initialization, pruning, and during learning, and answer questions on the relationship between the structure of Neural Networks and their performance. This includes the first work of inducing priors from network theory into Recurrent Neural Networks and an architectural performance prediction during a Neural Architecture Search. Within our experiments, we show how magnitude class blinded pruning achieves 97.5% on MNIST with 80% compression and re-training, which is 0.5 points more than without compression, that magnitude class uniform pruning is significantly inferior to it and how a genetic search enhanced with performance prediction achieves 82.4% on CIFAR10. Further, performance prediction for Recurrent Networks learning the Reber grammar shows an R^2 of up to 0.81 given only structural information.

Supervised training for real-world denoising presents challenges due to the difficulty of collecting large datasets of paired noisy and clean images. Recent methods have attempted to address this by utilizing unpaired datasets of clean and noisy images. Some approaches leverage such unpaired data to train denoisers in a supervised manner by generating synthetic clean-noisy pairs. However, these methods often fall short due to the distribution gap between synthetic and real noisy images. To mitigate this issue, we propose a solution based on input sparsification, specifically using random input masking. Our method, which we refer to as Mask, Inpaint and Denoise (MID), trains a denoiser to simultaneously denoise and inpaint synthetic clean-noisy pairs. On one hand, input sparsification reduces the gap between synthetic and real noisy images. On the other hand, an inpainter trained in a supervised manner can still accurately reconstruct sparse inputs by predicting missing clean pixels using the remaining unmasked pixels. Our approach begins with a synthetic Gaussian noise sampler and iteratively refines it using a noise dataset derived from the denoiser's predictions. The noise dataset is created by subtracting predicted pseudo-clean images from real noisy images at each iteration. The core intuition is that improving the denoiser results in a more accurate noise dataset and, consequently, a better noise sampler. We validate our method through extensive experiments on real-world noisy image datasets, demonstrating competitive performance compared to existing unsupervised denoising methods.

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are often best described using continuous-time stochastic processes. Unfortunately, most existing structure learning approaches assume that the underlying process evolves in discrete-time and/or observations occur at regular time intervals. These mismatched assumptions can often lead to incorrect learned structures and models. In this work, we introduce a novel structure learning method, SCOTCH, which combines neural stochastic differential equations (SDE) with variational inference to infer a posterior distribution over possible structures. This continuous-time approach can naturally handle both learning from and predicting observations at arbitrary time points. Theoretically, we establish sufficient conditions for an SDE and SCOTCH to be structurally identifiable, and prove its consistency under infinite data limits. Empirically, we demonstrate that our approach leads to improved structure learning performance on both synthetic and real-world datasets compared to relevant baselines under regular and irregular sampling intervals.

Periodic signals play an important role in daily lives. Although conventional sequential models have shown remarkable success in various fields, they still come short in modeling periodicity; they either collapse, diverge or ignore details. In this paper, we introduce a novel framework inspired by Fourier series to generate periodic signals. We first decompose the given signals into multiple sines and cosines and then conditionally generate periodic signals with the output components. We have shown our model efficacy on three tasks: reconstruction, imputation and conditional generation. Our model outperforms baselines in all tasks and shows more stable and refined results.

The noise transition matrix plays a central role in the problem of learning with noisy labels. Among many other reasons, a large number of existing solutions rely on access to it. Identifying and estimating the transition matrix without ground truth labels is a critical and challenging task. When label noise transition depends on each instance, the problem of identifying the instance-dependent noise transition matrix becomes substantially more challenging. Despite recent works proposing solutions for learning from instance-dependent noisy labels, the field lacks a unified understanding of when such a problem remains identifiable. The goal of this paper is to characterize the identifiability of the label noise transition matrix. Building on Kruskal's identifiability results, we are able to show the necessity of multiple noisy labels in identifying the noise transition matrix for the generic case at the instance level. We further instantiate the results to explain the successes of the state-of-the-art solutions and how additional assumptions alleviated the requirement of multiple noisy labels. Our result also reveals that disentangled features are helpful in the above identification task and we provide empirical evidence.

Diffusion models have shown a great ability at bridging the performance gap between predictive and generative approaches for speech enhancement. We have shown that they may even outperform their predictive counterparts for non-additive corruption types or when they are evaluated on mismatched conditions. However, diffusion models suffer from a high computational burden, mainly as they require to run a neural network for each reverse diffusion step, whereas predictive approaches only require one pass. As diffusion models are generative approaches they may also produce vocalizing and breathing artifacts in adverse conditions. In comparison, in such difficult scenarios, predictive models typically do not produce such artifacts but tend to distort the target speech instead, thereby degrading the speech quality. In this work, we present a stochastic regeneration approach where an estimate given by a predictive model is provided as a guide for further diffusion. We show that the proposed approach uses the predictive model to remove the vocalizing and breathing artifacts while producing very high quality samples thanks to the diffusion model, even in adverse conditions. We further show that this approach enables to use lighter sampling schemes with fewer diffusion steps without sacrificing quality, thus lifting the computational burden by an order of magnitude. Source code and audio examples are available online (https://uhh.de/inf-sp-storm).

Removing background noise from speech audio has been the subject of considerable effort, especially in recent years due to the rise of virtual communication and amateur recordings. Yet background noise is not the only unpleasant disturbance that can prevent intelligibility: reverb, clipping, codec artifacts, problematic equalization, limited bandwidth, or inconsistent loudness are equally disturbing and ubiquitous. In this work, we propose to consider the task of speech enhancement as a holistic endeavor, and present a universal speech enhancement system that tackles 55 different distortions at the same time. Our approach consists of a generative model that employs score-based diffusion, together with a multi-resolution conditioning network that performs enhancement with mixture density networks. We show that this approach significantly outperforms the state of the art in a subjective test performed by expert listeners. We also show that it achieves competitive objective scores with just 4-8 diffusion steps, despite not considering any particular strategy for fast sampling. We hope that both our methodology and technical contributions encourage researchers and practitioners to adopt a universal approach to speech enhancement, possibly framing it as a generative task.

We describe a novel approach for developing realistic digital models of dynamic range compressors for digital audio production by analyzing their analog prototypes. While realistic digital dynamic compressors are potentially useful for many applications, the design process is challenging because the compressors operate nonlinearly over long time scales. Our approach is based on the structured state space sequence model (S4), as implementing the state-space model (SSM) has proven to be efficient at learning long-range dependencies and is promising for modeling dynamic range compressors. We present in this paper a deep learning model with S4 layers to model the Teletronix LA-2A analog dynamic range compressor. The model is causal, executes efficiently in real time, and achieves roughly the same quality as previous deep-learning models but with fewer parameters.

Generative speech enhancement has recently shown promising advancements in improving speech quality in noisy environments. Multiple diffusion-based frameworks exist, each employing distinct training objectives and learning techniques. This paper aims at explaining the differences between these frameworks by focusing our investigation on score-based generative models and Schr\"odinger bridge. We conduct a series of comprehensive experiments to compare their performance and highlight differing training behaviors. Furthermore, we propose a novel perceptual loss function tailored for the Schr\"odinger bridge framework, demonstrating enhanced performance and improved perceptual quality of the enhanced speech signals. All experimental code and pre-trained models are publicly available to facilitate further research and development in this.

We present a causal speech enhancement model working on the raw waveform that runs in real-time on a laptop CPU. The proposed model is based on an encoder-decoder architecture with skip-connections. It is optimized on both time and frequency domains, using multiple loss functions. Empirical evidence shows that it is capable of removing various kinds of background noise including stationary and non-stationary noises, as well as room reverb. Additionally, we suggest a set of data augmentation techniques applied directly on the raw waveform which further improve model performance and its generalization abilities. We perform evaluations on several standard benchmarks, both using objective metrics and human judgements. The proposed model matches state-of-the-art performance of both causal and non causal methods while working directly on the raw waveform.

We bound the excess risk of interpolating deep linear networks trained using gradient flow. In a setting previously used to establish risk bounds for the minimum ell_2-norm interpolant, we show that randomly initialized deep linear networks can closely approximate or even match known bounds for the minimum ell_2-norm interpolant. Our analysis also reveals that interpolating deep linear models have exactly the same conditional variance as the minimum ell_2-norm solution. Since the noise affects the excess risk only through the conditional variance, this implies that depth does not improve the algorithm's ability to "hide the noise". Our simulations verify that aspects of our bounds reflect typical behavior for simple data distributions. We also find that similar phenomena are seen in simulations with ReLU networks, although the situation there is more nuanced.

We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs -- even in the case of 1-bit quantization -- allow a high accuracy approximation of the underlying kernels, and the approximation error decays at least polynomially fast as the dimension of the RFFs increases. We also show that the quantized RFFs can be further compressed, yielding an excellent trade-off between memory use and accuracy. Namely, the approximation error now decays exponentially as a function of the bits used. Moreover, we empirically show by testing the performance of our methods on several machine learning tasks that our method compares favorably to other state of the art quantization methods in this context.

Recent progress in separating the speech signals from multiple overlapping speakers using a single audio channel has brought us closer to solving the cocktail party problem. However, most studies in this area use a constrained problem setup, comparing performance when speakers overlap almost completely, at artificially low sampling rates, and with no external background noise. In this paper, we strive to move the field towards more realistic and challenging scenarios. To that end, we created the WSJ0 Hipster Ambient Mixtures (WHAM!) dataset, consisting of two speaker mixtures from the wsj0-2mix dataset combined with real ambient noise samples. The samples were collected in coffee shops, restaurants, and bars in the San Francisco Bay Area, and are made publicly available. We benchmark various speech separation architectures and objective functions to evaluate their robustness to noise. While separation performance decreases as a result of noise, we still observe substantial gains relative to the noisy signals for most approaches.

Large language models (LLMs) often produce inaccurate or misleading content-hallucinations. To address this challenge, we introduce Noise-Augmented Fine-Tuning (NoiseFiT), a novel framework that leverages adaptive noise injection based on the signal-to-noise ratio (SNR) to enhance model robustness. In particular, NoiseFiT selectively perturbs layers identified as either high-SNR (more robust) or low-SNR (potentially under-regularized) using a dynamically scaled Gaussian noise. We further propose a hybrid loss that combines standard cross-entropy, soft cross-entropy, and consistency regularization to ensure stable and accurate outputs under noisy training conditions. Our theoretical analysis shows that adaptive noise injection is both unbiased and variance-preserving, providing strong guarantees for convergence in expectation. Empirical results on multiple test and benchmark datasets demonstrate that NoiseFiT significantly reduces hallucination rates, often improving or matching baseline performance in key tasks. These findings highlight the promise of noise-driven strategies for achieving robust, trustworthy language modeling without incurring prohibitive computational overhead. Given the comprehensive and detailed nature of our experiments, we have publicly released the fine-tuning logs, benchmark evaluation artifacts, and source code online at W&B, Hugging Face, and GitHub, respectively, to foster further research, accessibility and reproducibility.

This paper studies sequence modeling for prediction tasks with long range dependencies. We propose a new formulation for state space models (SSMs) based on learning linear dynamical systems with the spectral filtering algorithm (Hazan et al. (2017)). This gives rise to a novel sequence prediction architecture we call a spectral state space model. Spectral state space models have two primary advantages. First, they have provable robustness properties as their performance depends on neither the spectrum of the underlying dynamics nor the dimensionality of the problem. Second, these models are constructed with fixed convolutional filters that do not require learning while still outperforming SSMs in both theory and practice. The resulting models are evaluated on synthetic dynamical systems and long-range prediction tasks of various modalities. These evaluations support the theoretical benefits of spectral filtering for tasks requiring very long range memory.

Inferring music time structures has a broad range of applications in music production, processing and analysis. Scholars have proposed various methods to analyze different aspects of time structures, such as beat, downbeat, tempo and meter. Many state-of-the-art (SOFA) methods, however, are computationally expensive. This makes them inapplicable in real-world industrial settings where the scale of the music collections can be millions. This paper proposes a new state space and a semi-Markov model for music time structure analysis. The proposed approach turns the commonly used 2D state spaces into a 1D model through a jump-back reward strategy. It reduces the state spaces size drastically. We then utilize the proposed method for causal, joint beat, downbeat, tempo, and meter tracking, and compare it against several previous methods. The proposed method delivers similar performance with the SOFA joint causal models with a much smaller state space and a more than 30 times speedup.

Privacy amplification exploits randomness in data selection to provide tighter differential privacy (DP) guarantees. This analysis is key to DP-SGD's success in machine learning, but, is not readily applicable to the newer state-of-the-art algorithms. This is because these algorithms, known as DP-FTRL, use the matrix mechanism to add correlated noise instead of independent noise as in DP-SGD. In this paper, we propose "MMCC", the first algorithm to analyze privacy amplification via sampling for any generic matrix mechanism. MMCC is nearly tight in that it approaches a lower bound as epsilonto0. To analyze correlated outputs in MMCC, we prove that they can be analyzed as if they were independent, by conditioning them on prior outputs. Our "conditional composition theorem" has broad utility: we use it to show that the noise added to binary-tree-DP-FTRL can asymptotically match the noise added to DP-SGD with amplification. Our amplification algorithm also has practical empirical utility: we show it leads to significant improvement in the privacy-utility trade-offs for DP-FTRL algorithms on standard benchmarks.

Electrocardiography (ECG) signals are often degraded by noise, which complicates diagnosis in clinical and wearable settings. This study proposes a diffusion-based framework for ECG noise quantification via reconstruction-based anomaly detection, addressing annotation inconsistencies and the limited generalizability of conventional methods. We introduce a distributional evaluation using the Wasserstein-1 distance (W_1), comparing the reconstruction error distributions between clean and noisy ECGs to mitigate inconsistent annotations. Our final model achieved robust noise quantification using only three reverse diffusion steps. The model recorded a macro-average W_1 score of 1.308 across the benchmarks, outperforming the next-best method by over 48%. External validations demonstrated strong generalizability, supporting the exclusion of low-quality segments to enhance diagnostic accuracy and enable timely clinical responses to signal degradation. The proposed method enhances clinical decision-making, diagnostic accuracy, and real-time ECG monitoring capabilities, supporting future advancements in clinical and wearable ECG applications.

Structured pruning is one of the most popular approaches to effectively compress the heavy deep neural networks (DNNs) into compact sub-networks while retaining performance. The existing methods suffer from multi-stage procedures along with significant engineering efforts and human expertise. The Only-Train-Once (OTO) series has been recently proposed to resolve the many pain points by streamlining the workflow by automatically conducting (i) search space generation, (ii) structured sparse optimization, and (iii) sub-network construction. However, the built-in sparse optimizers in the OTO series, i.e., the Half-Space Projected Gradient (HSPG) family, have limitations that require hyper-parameter tuning and the implicit controls of the sparsity exploration, consequently requires intervening by human expertise. To address such limitations, we propose a Hybrid Efficient Structured Sparse Optimizer (HESSO). HESSO could automatically and efficiently train a DNN to produce a high-performing subnetwork. Meanwhile, it is almost tuning-free and enjoys user-friendly integration for generic training applications. To address another common issue of irreversible performance collapse observed in pruning DNNs, we further propose a Corrective Redundant Identification Cycle (CRIC) for reliably identifying indispensable structures. We numerically demonstrate the efficacy of HESSO and its enhanced version HESSO-CRIC on a variety of applications ranging from computer vision to natural language processing, including large language model. The numerical results showcase that HESSO can achieve competitive even superior performance to varying state-of-the-arts and support most DNN architectures. Meanwhile, CRIC can effectively prevent the irreversible performance collapse and further enhance the performance of HESSO on certain applications. The code is available at https://github.com/microsoft/only_train_once.

In this paper, we point out suboptimal noise-data mapping leads to slow training of diffusion models. During diffusion training, current methods diffuse each image across the entire noise space, resulting in a mixture of all images at every point in the noise layer. We emphasize that this random mixture of noise-data mapping complicates the optimization of the denoising function in diffusion models. Drawing inspiration from the immiscible phenomenon in physics, we propose Immiscible Diffusion, a simple and effective method to improve the random mixture of noise-data mapping. In physics, miscibility can vary according to various intermolecular forces. Thus, immiscibility means that the mixing of the molecular sources is distinguishable. Inspired by this, we propose an assignment-then-diffusion training strategy. Specifically, prior to diffusing the image data into noise, we assign diffusion target noise for the image data by minimizing the total image-noise pair distance in a mini-batch. The assignment functions analogously to external forces to separate the diffuse-able areas of images, thus mitigating the inherent difficulties in diffusion training. Our approach is remarkably simple, requiring only one line of code to restrict the diffuse-able area for each image while preserving the Gaussian distribution of noise. This ensures that each image is projected only to nearby noise. To address the high complexity of the assignment algorithm, we employ a quantized-assignment method to reduce the computational overhead to a negligible level. Experiments demonstrate that our method achieve up to 3x faster training for consistency models and DDIM on the CIFAR dataset, and up to 1.3x faster on CelebA datasets for consistency models. Besides, we conduct thorough analysis about the Immiscible Diffusion, which sheds lights on how it improves diffusion training speed while improving the fidelity.

Unsupervised denoising is a crucial challenge in real-world imaging applications. Unsupervised deep-learning methods have demonstrated impressive performance on benchmarks based on synthetic noise. However, no metrics are available to evaluate these methods in an unsupervised fashion. This is highly problematic for the many practical applications where ground-truth clean images are not available. In this work, we propose two novel metrics: the unsupervised mean squared error (MSE) and the unsupervised peak signal-to-noise ratio (PSNR), which are computed using only noisy data. We provide a theoretical analysis of these metrics, showing that they are asymptotically consistent estimators of the supervised MSE and PSNR. Controlled numerical experiments with synthetic noise confirm that they provide accurate approximations in practice. We validate our approach on real-world data from two imaging modalities: videos in raw format and transmission electron microscopy. Our results demonstrate that the proposed metrics enable unsupervised evaluation of denoising methods based exclusively on noisy data.

We revisit the noisy binary search model of Karp and Kleinberg, in which we have n coins with unknown probabilities p_i that we can flip. The coins are sorted by increasing p_i, and we would like to find where the probability crosses (to within varepsilon) of a target value tau. This generalized the fixed-noise model of Burnashev and Zigangirov , in which p_i = 1{2} pm varepsilon, to a setting where coins near the target may be indistinguishable from it. Karp and Kleinberg showed that Theta(1{varepsilon^2} log n) samples are necessary and sufficient for this task. We produce a practical algorithm by solving two theoretical challenges: high-probability behavior and sharp constants. We give an algorithm that succeeds with probability 1-delta from \[ 1{C_{\tau, \varepsilon}} \cdot \left(\lg n + O(\log^{2/3} n \log^{1/3} 1{\delta} + \log 1{\delta})\right) \] samples, where C_{tau, varepsilon} is the optimal such constant achievable. For delta > n^{-o(1)} this is within 1 + o(1) of optimal, and for delta ll 1 it is the first bound within constant factors of optimal.

While deep convolutional neural networks (CNNs) have achieved impressive success in image denoising with additive white Gaussian noise (AWGN), their performance remains limited on real-world noisy photographs. The main reason is that their learned models are easy to overfit on the simplified AWGN model which deviates severely from the complicated real-world noise model. In order to improve the generalization ability of deep CNN denoisers, we suggest training a convolutional blind denoising network (CBDNet) with more realistic noise model and real-world noisy-clean image pairs. On the one hand, both signal-dependent noise and in-camera signal processing pipeline is considered to synthesize realistic noisy images. On the other hand, real-world noisy photographs and their nearly noise-free counterparts are also included to train our CBDNet. To further provide an interactive strategy to rectify denoising result conveniently, a noise estimation subnetwork with asymmetric learning to suppress under-estimation of noise level is embedded into CBDNet. Extensive experimental results on three datasets of real-world noisy photographs clearly demonstrate the superior performance of CBDNet over state-of-the-arts in terms of quantitative metrics and visual quality. The code has been made available at https://github.com/GuoShi28/CBDNet.

Recent advancements in deep learning have led to widespread use of techniques for audio content generation, notably employing Denoising Diffusion Probabilistic Models (DDPM) across various tasks. Among these, Foley Sound Synthesis is of particular interest for its role in applications for the creation of multimedia content. Given the temporal-dependent nature of sound, it is crucial to design generative models that can effectively handle the sequential modeling of audio samples. Selective State Space Models (SSMs) have recently been proposed as a valid alternative to previously proposed techniques, demonstrating competitive performance with lower computational complexity. In this paper, we introduce MambaFoley, a diffusion-based model that, to the best of our knowledge, is the first to leverage the recently proposed SSM known as Mamba for the Foley sound generation task. To evaluate the effectiveness of the proposed method, we compare it with a state-of-the-art Foley sound generative model using both objective and subjective analyses.

Autoregressive models are typically applied to sequences of discrete tokens, but recent research indicates that generating sequences of continuous embeddings in an autoregressive manner is also feasible. However, such Continuous Autoregressive Models (CAMs) can suffer from a decline in generation quality over extended sequences due to error accumulation during inference. We introduce a novel method to address this issue by injecting random noise into the input embeddings during training. This procedure makes the model robust against varying error levels at inference. We further reduce error accumulation through an inference procedure that introduces low-level noise. Experiments on musical audio generation show that CAM substantially outperforms existing autoregressive and non-autoregressive approaches while preserving audio quality over extended sequences. This work paves the way for generating continuous embeddings in a purely autoregressive setting, opening new possibilities for real-time and interactive generative applications.

The progress in modelling time series and, more generally, sequences of structured data has recently revamped research in anomaly detection. The task stands for identifying abnormal behaviors in financial series, IT systems, aerospace measurements, and the medical domain, where anomaly detection may aid in isolating cases of depression and attend the elderly. Anomaly detection in time series is a complex task since anomalies are rare due to highly non-linear temporal correlations and since the definition of anomalous is sometimes subjective. Here we propose the novel use of Hyperbolic uncertainty for Anomaly Detection (HypAD). HypAD learns self-supervisedly to reconstruct the input signal. We adopt best practices from the state-of-the-art to encode the sequence by an LSTM, jointly learned with a decoder to reconstruct the signal, with the aid of GAN critics. Uncertainty is estimated end-to-end by means of a hyperbolic neural network. By using uncertainty, HypAD may assess whether it is certain about the input signal but it fails to reconstruct it because this is anomalous; or whether the reconstruction error does not necessarily imply anomaly, as the model is uncertain, e.g. a complex but regular input signal. The novel key idea is that a detectable anomaly is one where the model is certain but it predicts wrongly. HypAD outperforms the current state-of-the-art for univariate anomaly detection on established benchmarks based on data from NASA, Yahoo, Numenta, Amazon, and Twitter. It also yields state-of-the-art performance on a multivariate dataset of anomaly activities in elderly home residences, and it outperforms the baseline on SWaT. Overall, HypAD yields the lowest false alarms at the best performance rate, thanks to successfully identifying detectable anomalies.

Input space reconstruction is an attractive representation learning paradigm. Despite interpretability of the reconstruction and generation, we identify a misalignment between learning by reconstruction, and learning for perception. We show that the former allocates a model's capacity towards a subspace of the data explaining the observed variance--a subspace with uninformative features for the latter. For example, the supervised TinyImagenet task with images projected onto the top subspace explaining 90\% of the pixel variance can be solved with 45\% test accuracy. Using the bottom subspace instead, accounting for only 20\% of the pixel variance, reaches 55\% test accuracy. The features for perception being learned last explains the need for long training time, e.g., with Masked Autoencoders. Learning by denoising is a popular strategy to alleviate that misalignment. We prove that while some noise strategies such as masking are indeed beneficial, others such as additive Gaussian noise are not. Yet, even in the case of masking, we find that the benefits vary as a function of the mask's shape, ratio, and the considered dataset. While tuning the noise strategy without knowledge of the perception task seems challenging, we provide first clues on how to detect if a noise strategy is never beneficial regardless of the perception task.

We propose a simple but effective training-free approach tailored to diffusion-based image-to-image translation. Our approach revises the original noise prediction network of a pretrained diffusion model by introducing a noise correction term. We formulate the noise correction term as the difference between two noise predictions; one is computed from the denoising network with a progressive interpolation of the source and target prompt embeddings, while the other is the noise prediction with the source prompt embedding. The final noise prediction network is given by a linear combination of the standard denoising term and the noise correction term, where the former is designed to reconstruct must-be-preserved regions while the latter aims to effectively edit regions of interest relevant to the target prompt. Our approach can be easily incorporated into existing image-to-image translation methods based on diffusion models. Extensive experiments verify that the proposed technique achieves outstanding performance with low latency and consistently improves existing frameworks when combined with them.

Recent work has shown how denoising and contractive autoencoders implicitly capture the structure of the data-generating density, in the case where the corruption noise is Gaussian, the reconstruction error is the squared error, and the data is continuous-valued. This has led to various proposals for sampling from this implicitly learned density function, using Langevin and Metropolis-Hastings MCMC. However, it remained unclear how to connect the training procedure of regularized auto-encoders to the implicit estimation of the underlying data-generating distribution when the data are discrete, or using other forms of corruption process and reconstruction errors. Another issue is the mathematical justification which is only valid in the limit of small corruption noise. We propose here a different attack on the problem, which deals with all these issues: arbitrary (but noisy enough) corruption, arbitrary reconstruction loss (seen as a log-likelihood), handling both discrete and continuous-valued variables, and removing the bias due to non-infinitesimal corruption noise (or non-infinitesimal contractive penalty).

The task of estimating the fundamental frequency of a monophonic sound recording, also known as pitch tracking, is fundamental to audio processing with multiple applications in speech processing and music information retrieval. To date, the best performing techniques, such as the pYIN algorithm, are based on a combination of DSP pipelines and heuristics. While such techniques perform very well on average, there remain many cases in which they fail to correctly estimate the pitch. In this paper, we propose a data-driven pitch tracking algorithm, CREPE, which is based on a deep convolutional neural network that operates directly on the time-domain waveform. We show that the proposed model produces state-of-the-art results, performing equally or better than pYIN. Furthermore, we evaluate the model's generalizability in terms of noise robustness. A pre-trained version of CREPE is made freely available as an open-source Python module for easy application.

This report presents the dataset and baseline of Task 3 of the DCASE2021 Challenge on Sound Event Localization and Detection (SELD). The dataset is based on emulation of real recordings of static or moving sound events under real conditions of reverberation and ambient noise, using spatial room impulse responses captured in a variety of rooms and delivered in two spatial formats. The acoustical synthesis remains the same as in the previous iteration of the challenge, however the new dataset brings more challenging conditions of polyphony and overlapping instances of the same class. The most important difference of the new dataset is the introduction of directional interferers, meaning sound events that are localized in space but do not belong to the target classes to be detected and are not annotated. Since such interfering events are expected in every real-world scenario of SELD, the new dataset aims to promote systems that deal with this condition effectively. A modified SELDnet baseline employing the recent ACCDOA representation of SELD problems accompanies the dataset and it is shown to outperform the previous one. The new dataset is shown to be significantly more challenging for both baselines according to all considered metrics. To investigate the individual and combined effects of ambient noise, interferers, and reverberation, we study the performance of the baseline on different versions of the dataset excluding or including combinations of these factors. The results indicate that by far the most detrimental effects are caused by directional interferers.

Denoising diffusion probabilistic models (DDPMs) (Ho et al. 2020) have shown impressive results on image and waveform generation in continuous state spaces. Here, we introduce Discrete Denoising Diffusion Probabilistic Models (D3PMs), diffusion-like generative models for discrete data that generalize the multinomial diffusion model of Hoogeboom et al. 2021, by going beyond corruption processes with uniform transition probabilities. This includes corruption with transition matrices that mimic Gaussian kernels in continuous space, matrices based on nearest neighbors in embedding space, and matrices that introduce absorbing states. The third allows us to draw a connection between diffusion models and autoregressive and mask-based generative models. We show that the choice of transition matrix is an important design decision that leads to improved results in image and text domains. We also introduce a new loss function that combines the variational lower bound with an auxiliary cross entropy loss. For text, this model class achieves strong results on character-level text generation while scaling to large vocabularies on LM1B. On the image dataset CIFAR-10, our models approach the sample quality and exceed the log-likelihood of the continuous-space DDPM model.

In a differentially private sequential learning setting, agents introduce endogenous noise into their actions to maintain privacy. Applying this to a standard sequential learning model leads to different outcomes for continuous vs. binary signals. For continuous signals with a nonzero privacy budget, we introduce a novel smoothed randomized response mechanism that adapts noise based on distance to a threshold, unlike traditional randomized response, which applies uniform noise. This enables agents' actions to better reflect both private signals and observed history, accelerating asymptotic learning speed to Theta_{epsilon}(log(n)), compared to Theta(log(n)) in the non-private regime where privacy budget is infinite. Moreover, in the non-private setting, the expected stopping time for the first correct decision and the number of incorrect actions diverge, meaning early agents may make mistakes for an unreasonably long period. In contrast, under a finite privacy budget epsilon in (0,1), both remain finite, highlighting a stark contrast between private and non-private learning. Learning with continuous signals in the private regime is more efficient, as smooth randomized response enhances the log-likelihood ratio over time, improving information aggregation. Conversely, for binary signals, differential privacy noise hinders learning, as agents tend to use a constant randomized response strategy before an information cascade forms, reducing action informativeness and hampering the overall process.

Tweedie distributions are a special case of exponential dispersion models, which are often used in classical statistics as distributions for generalized linear models. Here, we reveal that Tweedie distributions also play key roles in modern deep learning era, leading to a distribution independent self-supervised image denoising formula without clean reference images. Specifically, by combining with the recent Noise2Score self-supervised image denoising approach and the saddle point approximation of Tweedie distribution, we can provide a general closed-form denoising formula that can be used for large classes of noise distributions without ever knowing the underlying noise distribution. Similar to the original Noise2Score, the new approach is composed of two successive steps: score matching using perturbed noisy images, followed by a closed form image denoising formula via distribution-independent Tweedie's formula. This also suggests a systematic algorithm to estimate the noise model and noise parameters for a given noisy image data set. Through extensive experiments, we demonstrate that the proposed method can accurately estimate noise models and parameters, and provide the state-of-the-art self-supervised image denoising performance in the benchmark dataset and real-world dataset.

Pruning is a model compression method that removes redundant parameters in deep neural networks (DNNs) while maintaining accuracy. Most available filter pruning methods require complex treatments such as iterative pruning, features statistics/ranking, or additional optimization designs in the training process. In this paper, we propose a simple and effective regularization strategy from a new perspective of evolution of features, which we call feature flow regularization (FFR), for improving structured sparsity and filter pruning in DNNs. Specifically, FFR imposes controls on the gradient and curvature of feature flow along the neural network, which implicitly increases the sparsity of the parameters. The principle behind FFR is that coherent and smooth evolution of features will lead to an efficient network that avoids redundant parameters. The high structured sparsity obtained from FFR enables us to prune filters effectively. Experiments with VGGNets, ResNets on CIFAR-10/100, and Tiny ImageNet datasets demonstrate that FFR can significantly improve both unstructured and structured sparsity. Our pruning results in terms of reduction of parameters and FLOPs are comparable to or even better than those of state-of-the-art pruning methods.

Reconstruction of magnetic resonance imaging (MRI) data has been positively affected by deep learning. A key challenge remains: to improve generalisation to distribution shifts between the training and testing data. Most approaches aim to address this via inductive design or data augmentation. However, they can be affected by misleading data, e.g. random noise, and cases where the inference stage data do not match assumptions in the modelled shifts. In this work, by employing a conditional hyperparameter network, we eliminate the need of augmentation, yet maintain robust performance under various levels of Gaussian noise. We demonstrate that our model withstands various input noise levels while producing high-definition reconstructions during the test stage. Moreover, we present a hyperparameter sampling strategy that accelerates the convergence of training. Our proposed method achieves the highest accuracy and image quality in all settings compared to baseline methods.

We consider the learning from noisy labels (NL) problem which emerges in many real-world applications. In addition to the widely-studied synthetic noise in the NL literature, we also consider the pseudo labels in semi-supervised learning (Semi-SL) as a special case of NL. For both types of noise, we argue that the generalization performance of existing methods is highly coupled with the quality of noisy labels. Therefore, we counter the problem from a novel and unified perspective: learning from the auxiliary clean labels. Specifically, we propose the Rotational-Decoupling Consistency Regularization (RDCR) framework that integrates the consistency-based methods with the self-supervised rotation task to learn noise-tolerant representations. The experiments show that RDCR achieves comparable or superior performance than the state-of-the-art methods under small noise, while outperforms the existing methods significantly when there is large noise.

Diffusion models have recently achieved great success in the synthesis of high-quality images and videos. However, the existing denoising techniques in diffusion models are commonly based on step-by-step noise predictions, which suffers from high computation cost, resulting in a prohibitive latency for interactive applications. In this paper, we propose AdaptiveDiffusion to relieve this bottleneck by adaptively reducing the noise prediction steps during the denoising process. Our method considers the potential of skipping as many noise prediction steps as possible while keeping the final denoised results identical to the original full-step ones. Specifically, the skipping strategy is guided by the third-order latent difference that indicates the stability between timesteps during the denoising process, which benefits the reusing of previous noise prediction results. Extensive experiments on image and video diffusion models demonstrate that our method can significantly speed up the denoising process while generating identical results to the original process, achieving up to an average 2~5x speedup without quality degradation.

Diffusion models have achieved state-of-the-art synthesis quality on both visual and audio tasks, and recent works further adapt them to textual data by diffusing on the embedding space. In this paper, we conduct systematic studies and analyze the challenges between the continuous data space and the embedding space which have not been carefully explored. Firstly, the data distribution is learnable for embeddings, which may lead to the collapse of the loss function. Secondly, as the norm of embeddings varies between popular and rare words, adding the same noise scale will lead to sub-optimal results. In addition, we find the normal level of noise causes insufficient training of the model. To address the above challenges, we propose Difformer, an embedding diffusion model based on Transformer, which consists of three essential modules including an additional anchor loss function, a layer normalization module for embeddings, and a noise factor to the Gaussian noise. Experiments on two seminal text generation tasks including machine translation and text summarization show the superiority of Difformer over compared embedding diffusion baselines.

Recent advancements in music generation have garnered significant attention, yet existing approaches face critical limitations. Some current generative models can only synthesize either the vocal track or the accompaniment track. While some models can generate combined vocal and accompaniment, they typically rely on meticulously designed multi-stage cascading architectures and intricate data pipelines, hindering scalability. Additionally, most systems are restricted to generating short musical segments rather than full-length songs. Furthermore, widely used language model-based methods suffer from slow inference speeds. To address these challenges, we propose DiffRhythm, the first latent diffusion-based song generation model capable of synthesizing complete songs with both vocal and accompaniment for durations of up to 4m45s in only ten seconds, maintaining high musicality and intelligibility. Despite its remarkable capabilities, DiffRhythm is designed to be simple and elegant: it eliminates the need for complex data preparation, employs a straightforward model structure, and requires only lyrics and a style prompt during inference. Additionally, its non-autoregressive structure ensures fast inference speeds. This simplicity guarantees the scalability of DiffRhythm. Moreover, we release the complete training code along with the pre-trained model on large-scale data to promote reproducibility and further research.

Diffusion models achieved great success in image synthesis, but still face challenges in high-resolution generation. Through the lens of discrete cosine transformation, we find the main reason is that the same noise level on a higher resolution results in a higher Signal-to-Noise Ratio in the frequency domain. In this work, we present Relay Diffusion Model (RDM), which transfers a low-resolution image or noise into an equivalent high-resolution one for diffusion model via blurring diffusion and block noise. Therefore, the diffusion process can continue seamlessly in any new resolution or model without restarting from pure noise or low-resolution conditioning. RDM achieves state-of-the-art FID on CelebA-HQ and sFID on ImageNet 256times256, surpassing previous works such as ADM, LDM and DiT by a large margin. All the codes and checkpoints are open-sourced at https://github.com/THUDM/RelayDiffusion.

Deep Image Prior (DIP) shows that some network architectures naturally bias towards smooth images and resist noises, a phenomenon known as spectral bias. Image denoising is an immediate application of this property. Although DIP has removed the requirement of large training sets, it still presents two practical challenges for denoising: architectural design and noise-fitting, which are often intertwined. Existing methods mostly handcraft or search for the architecture from a large design space, due to the lack of understanding on how the architectural choice corresponds to the image. In this study, we analyze from a frequency perspective to demonstrate that the unlearnt upsampling is the main driving force behind the denoising phenomenon in DIP. This finding then leads to strategies for estimating a suitable architecture for every image without a laborious search. Extensive experiments show that the estimated architectures denoise and preserve the textural details better than current methods with up to 95% fewer parameters. The under-parameterized nature also makes them especially robust to a higher level of noise.

In order to improve the quality of synthesized videos, currently, one predominant method involves retraining an expert diffusion model and then implementing a noising-denoising process for refinement. Despite the significant training costs, maintaining consistency of content between the original and enhanced videos remains a major challenge. To tackle this challenge, we propose a novel formulation that considers both visual quality and consistency of content. Consistency of content is ensured by a proposed loss function that maintains the structure of the input, while visual quality is improved by utilizing the denoising process of pretrained diffusion models. To address the formulated optimization problem, we have developed a plug-and-play noise optimization strategy, referred to as Noise Calibration. By refining the initial random noise through a few iterations, the content of original video can be largely preserved, and the enhancement effect demonstrates a notable improvement. Extensive experiments have demonstrated the effectiveness of the proposed method.

Recently, conditional score-based diffusion models have gained significant attention in the field of supervised speech enhancement, yielding state-of-the-art performance. However, these methods may face challenges when generalising to unseen conditions. To address this issue, we introduce an alternative approach that operates in an unsupervised manner, leveraging the generative power of diffusion models. Specifically, in a training phase, a clean speech prior distribution is learnt in the short-time Fourier transform (STFT) domain using score-based diffusion models, allowing it to unconditionally generate clean speech from Gaussian noise. Then, we develop a posterior sampling methodology for speech enhancement by combining the learnt clean speech prior with a noise model for speech signal inference. The noise parameters are simultaneously learnt along with clean speech estimation through an iterative expectationmaximisation (EM) approach. To the best of our knowledge, this is the first work exploring diffusion-based generative models for unsupervised speech enhancement, demonstrating promising results compared to a recent variational auto-encoder (VAE)-based unsupervised approach and a state-of-the-art diffusion-based supervised method. It thus opens a new direction for future research in unsupervised speech enhancement.

Formalized in ISO 12913, the "soundscape" approach is a paradigmatic shift towards perception-based urban sound management, aiming to alleviate the substantial socioeconomic costs of noise pollution to advance the United Nations Sustainable Development Goals. Focusing on traffic-exposed outdoor residential sites, we implemented an automatic masker selection system (AMSS) utilizing natural sounds to mask (or augment) traffic soundscapes. We employed a pre-trained AI model to automatically select the optimal masker and adjust its playback level, adapting to changes over time in the ambient environment to maximize "Pleasantness", a perceptual dimension of soundscape quality in ISO 12913. Our validation study involving (N=68) residents revealed a significant 14.6 % enhancement in "Pleasantness" after intervention, correlating with increased restorativeness and positive affect. Perceptual enhancements at the traffic-exposed site matched those at a quieter control site with 6 dB(A) lower L_A,eq and road traffic noise dominance, affirming the efficacy of AMSS as a soundscape intervention, while streamlining the labour-intensive assessment of "Pleasantness" with probabilistic AI prediction.

Deep learning classifiers face significant challenges when dealing with heterogeneous multi-modal and multi-organ biomedical datasets. The low-level feature distinguishability limited to imaging-modality hinders the classifiers' ability to learn high-level semantic relationships, resulting in sub-optimal performance. To address this issue, image augmentation strategies are employed as regularization techniques. While additive noise input during network training is a well-established augmentation as regularization method, modern pipelines often favor more robust techniques such as dropout and weight decay. This preference stems from the observation that combining these established techniques with noise input can adversely affect model performance. In this study, we propose a novel pretraining pipeline that learns to generate conditional noise mask specifically tailored to improve performance on multi-modal and multi-organ datasets. As a reinforcement learning algorithm, our approach employs a dual-component system comprising a very light-weight policy network that learns to sample conditional noise using a differentiable beta distribution as well as a classifier network. The policy network is trained using the reinforce algorithm to generate image-specific noise masks that regularize the classifier during pretraining. A key aspect is that the policy network's role is limited to obtaining an intermediate (or heated) model before fine-tuning. During inference, the policy network is omitted, allowing direct comparison between the baseline and noise-regularized models. We conducted experiments and related analyses on RadImageNet datasets. Results demonstrate that fine-tuning the intermediate models consistently outperforms conventional training algorithms on both classification and generalization to unseen concept tasks.

We look at the eigenvalues of the Hessian of a loss function before and after training. The eigenvalue distribution is seen to be composed of two parts, the bulk which is concentrated around zero, and the edges which are scattered away from zero. We present empirical evidence for the bulk indicating how over-parametrized the system is, and for the edges that depend on the input data.

This paper studies Kernel density estimation for a high-dimensional distribution rho(x). Traditional approaches have focused on the limit of large number of data points n and fixed dimension d. We analyze instead the regime where both the number n of data points y_i and their dimensionality d grow with a fixed ratio alpha=(log n)/d. Our study reveals three distinct statistical regimes for the kernel-based estimate of the density hat rho_h^{D}(x)=1{n h^d}sum_{i=1}^n Kleft(x-y_i{h}right), depending on the bandwidth h: a classical regime for large bandwidth where the Central Limit Theorem (CLT) holds, which is akin to the one found in traditional approaches. Below a certain value of the bandwidth, h_{CLT}(alpha), we find that the CLT breaks down. The statistics of hat rho_h^{D}(x) for a fixed x drawn from rho(x) is given by a heavy-tailed distribution (an alpha-stable distribution). In particular below a value h_G(alpha), we find that hat rho_h^{D}(x) is governed by extreme value statistics: only a few points in the database matter and give the dominant contribution to the density estimator. We provide a detailed analysis for high-dimensional multivariate Gaussian data. We show that the optimal bandwidth threshold based on Kullback-Leibler divergence lies in the new statistical regime identified in this paper. Our findings reveal limitations of classical approaches, show the relevance of these new statistical regimes, and offer new insights for Kernel density estimation in high-dimensional settings.

In this work, we theoretically investigate the generalization properties of neural networks (NN) trained by stochastic gradient descent (SGD) algorithm with large learning rates. Under such a training regime, our finding is that, the oscillation of the NN weights caused by the large learning rate SGD training turns out to be beneficial to the generalization of the NN, which potentially improves over the same NN trained by SGD with small learning rates that converges more smoothly. In view of this finding, we call such a phenomenon "benign oscillation". Our theory towards demystifying such a phenomenon builds upon the feature learning perspective of deep learning. Specifically, we consider a feature-noise data generation model that consists of (i) weak features which have a small ell_2-norm and appear in each data point; (ii) strong features which have a larger ell_2-norm but only appear in a certain fraction of all data points; and (iii) noise. We prove that NNs trained by oscillating SGD with a large learning rate can effectively learn the weak features in the presence of those strong features. In contrast, NNs trained by SGD with a small learning rate can only learn the strong features but makes little progress in learning the weak features. Consequently, when it comes to the new testing data which consist of only weak features, the NN trained by oscillating SGD with a large learning rate could still make correct predictions consistently, while the NN trained by small learning rate SGD fails. Our theory sheds light on how large learning rate training benefits the generalization of NNs. Experimental results demonstrate our finding on "benign oscillation".

With its significant performance improvements, the deep learning paradigm has become a standard tool for modern image denoisers. While promising performance has been shown on seen noise distributions, existing approaches often suffer from generalisation to unseen noise types or general and real noise. It is understandable as the model is designed to learn paired mapping (e.g. from a noisy image to its clean version). In this paper, we instead propose to learn to disentangle the noisy image, under the intuitive assumption that different corrupted versions of the same clean image share a common latent space. A self-supervised learning framework is proposed to achieve the goal, without looking at the latent clean image. By taking two different corrupted versions of the same image as input, the proposed Multi-view Self-supervised Disentanglement (MeD) approach learns to disentangle the latent clean features from the corruptions and recover the clean image consequently. Extensive experimental analysis on both synthetic and real noise shows the superiority of the proposed method over prior self-supervised approaches, especially on unseen novel noise types. On real noise, the proposed method even outperforms its supervised counterparts by over 3 dB.

This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear system Atheta = b for which A and b can only be accessed through random estimates {({bf A}_n, {bf b}_n): n in N^*}. Our analysis is based on new results regarding moments and high probability bounds for products of matrices which are shown to be tight. We derive high probability bounds on the performance of LSA under weaker conditions on the sequence {({bf A}_n, {bf b}_n): n in N^*} than previous works. However, in contrast, we establish polynomial concentration bounds with order depending on the stepsize. We show that our conclusions cannot be improved without additional assumptions on the sequence of random matrices {{bf A}_n: n in N^*}, and in particular that no Gaussian or exponential high probability bounds can hold. Finally, we pay a particular attention to establishing bounds with sharp order with respect to the number of iterations and the stepsize and whose leading terms contain the covariance matrices appearing in the central limit theorems.

We introduce a theoretical framework for sampling from unnormalized densities based on a smoothing scheme that uses an isotropic Gaussian kernel with a single fixed noise scale. We prove one can decompose sampling from a density (minimal assumptions made on the density) into a sequence of sampling from log-concave conditional densities via accumulation of noisy measurements with equal noise levels. Our construction is unique in that it keeps track of a history of samples, making it non-Markovian as a whole, but it is lightweight algorithmically as the history only shows up in the form of a running empirical mean of samples. Our sampling algorithm generalizes walk-jump sampling (Saremi & Hyv\"arinen, 2019). The "walk" phase becomes a (non-Markovian) chain of (log-concave) Markov chains. The "jump" from the accumulated measurements is obtained by empirical Bayes. We study our sampling algorithm quantitatively using the 2-Wasserstein metric and compare it with various Langevin MCMC algorithms. We also report a remarkable capacity of our algorithm to "tunnel" between modes of a distribution.

Structural neural network pruning aims to remove the redundant channels in the deep convolutional neural networks (CNNs) by pruning the filters of less importance to the final output accuracy. To reduce the degradation of performance after pruning, many methods utilize the loss with sparse regularization to produce structured sparsity. In this paper, we analyze these sparsity-training-based methods and find that the regularization of unpruned channels is unnecessary. Moreover, it restricts the network's capacity, which leads to under-fitting. To solve this problem, we propose a novel pruning method, named MaskSparsity, with pruning-aware sparse regularization. MaskSparsity imposes the fine-grained sparse regularization on the specific filters selected by a pruning mask, rather than all the filters of the model. Before the fine-grained sparse regularization of MaskSparity, we can use many methods to get the pruning mask, such as running the global sparse regularization. MaskSparsity achieves 63.03%-FLOPs reduction on ResNet-110 by removing 60.34% of the parameters, with no top-1 accuracy loss on CIFAR-10. On ILSVRC-2012, MaskSparsity reduces more than 51.07% FLOPs on ResNet-50, with only a loss of 0.76% in the top-1 accuracy. The code is released at https://github.com/CASIA-IVA-Lab/MaskSparsity. Moreover, we have integrated the code of MaskSparity into a PyTorch pruning toolkit, EasyPruner, at https://gitee.com/casia_iva_engineer/easypruner.

While 2D diffusion models generate realistic, high-detail images, 3D shape generation methods like Score Distillation Sampling (SDS) built on these 2D diffusion models produce cartoon-like, over-smoothed shapes. To help explain this discrepancy, we show that the image guidance used in Score Distillation can be understood as the velocity field of a 2D denoising generative process, up to the choice of a noise term. In particular, after a change of variables, SDS resembles a high-variance version of Denoising Diffusion Implicit Models (DDIM) with a differently-sampled noise term: SDS introduces noise i.i.d. randomly at each step, while DDIM infers it from the previous noise predictions. This excessive variance can lead to over-smoothing and unrealistic outputs. We show that a better noise approximation can be recovered by inverting DDIM in each SDS update step. This modification makes SDS's generative process for 2D images almost identical to DDIM. In 3D, it removes over-smoothing, preserves higher-frequency detail, and brings the generation quality closer to that of 2D samplers. Experimentally, our method achieves better or similar 3D generation quality compared to other state-of-the-art Score Distillation methods, all without training additional neural networks or multi-view supervision, and providing useful insights into relationship between 2D and 3D asset generation with diffusion models.

While diffusion models have achieved great success in generating continuous signals such as images and audio, it remains elusive for diffusion models in learning discrete sequence data like natural languages. Although recent advances circumvent this challenge of discreteness by embedding discrete tokens as continuous surrogates, they still fall short of satisfactory generation quality. To understand this, we first dive deep into the denoised training protocol of diffusion-based sequence generative models and determine their three severe problems, i.e., 1) failing to learn, 2) lack of scalability, and 3) neglecting source conditions. We argue that these problems can be boiled down to the pitfall of the not completely eliminated discreteness in the embedding space, and the scale of noises is decisive herein. In this paper, we introduce DINOISER to facilitate diffusion models for sequence generation by manipulating noises. We propose to adaptively determine the range of sampled noise scales for counter-discreteness training; and encourage the proposed diffused sequence learner to leverage source conditions with amplified noise scales during inference. Experiments show that DINOISER enables consistent improvement over the baselines of previous diffusion-based sequence generative models on several conditional sequence modeling benchmarks thanks to both effective training and inference strategies. Analyses further verify that DINOISER can make better use of source conditions to govern its generative process.

Speech sounds convey a great deal of information about the scenes, resulting in a variety of effects ranging from reverberation to additional ambient sounds. In this paper, we manipulate input speech to sound as though it was recorded within a different scene, given an audio-visual conditional example recorded from that scene. Our model learns through self-supervision, taking advantage of the fact that natural video contains recurring sound events and textures. We extract an audio clip from a video and apply speech enhancement. We then train a latent diffusion model to recover the original speech, using another audio-visual clip taken from elsewhere in the video as a conditional hint. Through this process, the model learns to transfer the conditional example's sound properties to the input speech. We show that our model can be successfully trained using unlabeled, in-the-wild videos, and that an additional visual signal can improve its sound prediction abilities. Please see our project webpage for video results: https://tinglok.netlify.app/files/avsoundscape/

This paper explores the scenarios under which an attacker can claim that 'Noise and access to the softmax layer of the model is all you need' to steal the weights of a convolutional neural network whose architecture is already known. We were able to achieve 96% test accuracy using the stolen MNIST model and 82% accuracy using the stolen KMNIST model learned using only i.i.d. Bernoulli noise inputs. We posit that this theft-susceptibility of the weights is indicative of the complexity of the dataset and propose a new metric that captures the same. The goal of this dissemination is to not just showcase how far knowing the architecture can take you in terms of model stealing, but to also draw attention to this rather idiosyncratic weight learnability aspects of CNNs spurred by i.i.d. noise input. We also disseminate some initial results obtained with using the Ising probability distribution in lieu of the i.i.d. Bernoulli distribution.

Diffusion models are a family of generative models that yield record-breaking performance in tasks such as image synthesis, video generation, and molecule design. Despite their capabilities, their efficiency, especially in the reverse denoising process, remains a challenge due to slow convergence rates and high computational costs. In this work, we introduce an approach that leverages continuous dynamical systems to design a novel denoising network for diffusion models that is more parameter-efficient, exhibits faster convergence, and demonstrates increased noise robustness. Experimenting with denoising probabilistic diffusion models, our framework operates with approximately a quarter of the parameters and 30% of the Floating Point Operations (FLOPs) compared to standard U-Nets in Denoising Diffusion Probabilistic Models (DDPMs). Furthermore, our model is up to 70% faster in inference than the baseline models when measured in equal conditions while converging to better quality solutions.

Recently, research on denoising diffusion models has expanded its application to the field of image restoration. Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the reverse generation process, without modifying the original denoising diffusion process. However, since the degraded images already include low-frequency information, starting from Gaussian white noise will result in increased sampling steps. We propose Resfusion, a general framework that incorporates the residual term into the diffusion forward process, starting the reverse process directly from the noisy degraded images. The form of our inference process is consistent with the DDPM. We introduced a weighted residual noise, named resnoise, as the prediction target and explicitly provide the quantitative relationship between the residual term and the noise term in resnoise. By leveraging a smooth equivalence transformation, Resfusion determine the optimal acceleration step and maintains the integrity of existing noise schedules, unifying the training and inference processes. The experimental results demonstrate that Resfusion exhibits competitive performance on ISTD dataset, LOL dataset and Raindrop dataset with only five sampling steps. Furthermore, Resfusion can be easily applied to image generation and emerges with strong versatility. Our code and model are available at https://github.com/nkicsl/Resfusion.

In this paper, we propose to unify the two aspects of voice synthesis, namely text-to-speech (TTS) and vocoder, into one framework based on a pair of forward and reverse-time linear stochastic differential equations (SDE). The solutions of this SDE pair are two stochastic processes, one of which turns the distribution of mel spectrogram (or wave), that we want to generate, into a simple and tractable distribution. The other is the generation procedure that turns this tractable simple signal into the target mel spectrogram (or wave). The model that generates mel spectrogram is called It\^oTTS, and the model that generates wave is called It\^oWave. It\^oTTS and It\^oWave use the Wiener process as a driver to gradually subtract the excess signal from the noise signal to generate realistic corresponding meaningful mel spectrogram and audio respectively, under the conditional inputs of original text or mel spectrogram. The results of the experiment show that the mean opinion scores (MOS) of It\^oTTS and It\^oWave can exceed the current state-of-the-art methods, and reached 3.925pm0.160 and 4.35pm0.115 respectively. The generated audio samples are available at https://wushoule.github.io/ItoAudio/. All authors contribute equally to this work.

In recent years, denoising diffusion models have become a crucial area of research due to their abundance in the rapidly expanding field of generative AI. While recent statistical advances have delivered explanations for the generation ability of idealised denoising diffusion models for high-dimensional target data, implementations introduce thresholding procedures for the generating process to overcome issues arising from the unbounded state space of such models. This mismatch between theoretical design and implementation of diffusion models has been addressed empirically by using a reflected diffusion process as the driver of noise instead. In this paper, we study statistical guarantees of these denoising reflected diffusion models. In particular, we establish minimax optimal rates of convergence in total variation, up to a polylogarithmic factor, under Sobolev smoothness assumptions. Our main contributions include the statistical analysis of this novel class of denoising reflected diffusion models and a refined score approximation method in both time and space, leveraging spectral decomposition and rigorous neural network analysis.

Spatial audio quality is a highly multifaceted concept, with many interactions between environmental, geometrical, anatomical, psychological, and contextual considerations. Methods for characterization or evaluation of the geometrical components of spatial audio quality, however, remain scarce, despite being perhaps the least subjective aspect of spatial audio quality to quantify. By considering interchannel time and level differences relative to a reference signal, it is possible to construct a signal model to isolate some of the spatial distortion. By using a combination of least-square optimization and heuristics, we propose a signal decomposition method to isolate the spatial error from a processed signal, in terms of interchannel gain leakages and changes in relative delays. This allows the computation of simple energy-ratio metrics, providing objective measures of spatial and non-spatial signal qualities, with minimal assumptions and no dataset dependency. Experiments demonstrate the robustness of the method against common spatial signal degradation introduced by, e.g., audio compression and music source separation. Implementation is available at https://github.com/karnwatcharasupat/spauq.

The quality of generative models depends on the quality of the data they are trained on. Creating large-scale, high-quality datasets is often expensive and sometimes impossible, e.g. in certain scientific applications where there is no access to clean data due to physical or instrumentation constraints. Ambient Diffusion and related frameworks train diffusion models with solely corrupted data (which are usually cheaper to acquire) but ambient models significantly underperform models trained on clean data. We study this phenomenon at scale by training more than 80 models on data with different corruption levels across three datasets ranging from 30,000 to approx 1.3M samples. We show that it is impossible, at these sample sizes, to match the performance of models trained on clean data when only training on noisy data. Yet, a combination of a small set of clean data (e.g.~10% of the total dataset) and a large set of highly noisy data suffices to reach the performance of models trained solely on similar-size datasets of clean data, and in particular to achieve near state-of-the-art performance. We provide theoretical evidence for our findings by developing novel sample complexity bounds for learning from Gaussian Mixtures with heterogeneous variances. Our theoretical model suggests that, for large enough datasets, the effective marginal utility of a noisy sample is exponentially worse than that of a clean sample. Providing a small set of clean samples can significantly reduce the sample size requirements for noisy data, as we also observe in our experiments.

Federated learning (FL) leverages client-server communications to train global models on decentralized data. However, communication noise or errors can impair model accuracy. To address this problem, we propose a novel FL algorithm that enhances robustness against communication noise while also reducing communication load. We derive the proposed algorithm through solving the weighted least-squares (WLS) regression problem as an illustrative example. We first frame WLS regression as a distributed convex optimization problem over a federated network employing random scheduling for improved communication efficiency. We then apply the alternating direction method of multipliers (ADMM) to iteratively solve this problem. To counteract the detrimental effects of cumulative communication noise, we introduce a key modification by eliminating the dual variable and implementing a new local model update at each participating client. This subtle yet effective change results in using a single noisy global model update at each client instead of two, improving robustness against additive communication noise. Furthermore, we incorporate another modification enabling clients to continue local updates even when not selected by the server, leading to substantial performance improvements. Our theoretical analysis confirms the convergence of our algorithm in both mean and the mean-square senses, even when the server communicates with a random subset of clients over noisy links at each iteration. Numerical results validate the effectiveness of our proposed algorithm and corroborate our theoretical findings.

Denoising Diffusion Probabilistic Models (DDPMs) achieve state-of-the-art performance in synthesizing new images from random noise, but they lack meaningful latent space that encodes data into features. Recent DDPM-based editing techniques try to mitigate this issue by inverting images back to their approximated staring noise. In this work, we study the relation between the initial Gaussian noise, the samples generated from it, and their corresponding latent encodings obtained through the inversion procedure. First, we interpret their spatial distance relations to show the inaccuracy of the DDIM inversion technique by localizing latent representations manifold between the initial noise and generated samples. Then, we demonstrate the peculiar relation between initial Gaussian noise and its corresponding generations during diffusion training, showing that the high-level features of generated images stabilize rapidly, keeping the spatial distance relationship between noises and generations consistent throughout the training.

Conformal prediction is a widely used method to quantify the uncertainty of a classifier under the assumption of exchangeability (e.g., IID data). We generalize conformal prediction to the Hidden Markov Model (HMM) framework where the assumption of exchangeability is not valid. The key idea of the proposed method is to partition the non-exchangeable Markovian data from the HMM into exchangeable blocks by exploiting the de Finetti's Theorem for Markov Chains discovered by Diaconis and Freedman (1980). The permutations of the exchangeable blocks are viewed as randomizations of the observed Markovian data from the HMM. The proposed method provably retains all desirable theoretical guarantees offered by the classical conformal prediction framework in both exchangeable and Markovian settings. In particular, while the lack of exchangeability introduced by Markovian samples constitutes a violation of a crucial assumption for classical conformal prediction, the proposed method views it as an advantage that can be exploited to improve the performance further. Detailed numerical and empirical results that complement the theoretical conclusions are provided to illustrate the practical feasibility of the proposed method.

Denoising diffusion models, a class of generative models, have garnered immense interest lately in various deep-learning problems. A diffusion probabilistic model defines a forward diffusion stage where the input data is gradually perturbed over several steps by adding Gaussian noise and then learns to reverse the diffusion process to retrieve the desired noise-free data from noisy data samples. Diffusion models are widely appreciated for their strong mode coverage and quality of the generated samples despite their known computational burdens. Capitalizing on the advances in computer vision, the field of medical imaging has also observed a growing interest in diffusion models. To help the researcher navigate this profusion, this survey intends to provide a comprehensive overview of diffusion models in the discipline of medical image analysis. Specifically, we introduce the solid theoretical foundation and fundamental concepts behind diffusion models and the three generic diffusion modelling frameworks: diffusion probabilistic models, noise-conditioned score networks, and stochastic differential equations. Then, we provide a systematic taxonomy of diffusion models in the medical domain and propose a multi-perspective categorization based on their application, imaging modality, organ of interest, and algorithms. To this end, we cover extensive applications of diffusion models in the medical domain. Furthermore, we emphasize the practical use case of some selected approaches, and then we discuss the limitations of the diffusion models in the medical domain and propose several directions to fulfill the demands of this field. Finally, we gather the overviewed studies with their available open-source implementations at https://github.com/amirhossein-kz/Awesome-Diffusion-Models-in-Medical-Imaging.

We establish a new theoretical framework for learning under multi-class, instance-dependent label noise. This framework casts learning with label noise as a form of domain adaptation, in particular, domain adaptation under posterior drift. We introduce the concept of relative signal strength (RSS), a pointwise measure that quantifies the transferability from noisy to clean posterior. Using RSS, we establish nearly matching upper and lower bounds on the excess risk. Our theoretical findings support the simple Noise Ignorant Empirical Risk Minimization (NI-ERM) principle, which minimizes empirical risk while ignoring label noise. Finally, we translate this theoretical insight into practice: by using NI-ERM to fit a linear classifier on top of a self-supervised feature extractor, we achieve state-of-the-art performance on the CIFAR-N data challenge.

Denoising and filtering are widely used in routine seismic-data-processing to improve the signal-to-noise ratio (SNR) of recorded signals and by doing so to improve subsequent analyses. In this paper we develop a new denoising/decomposition method, DeepDenoiser, based on a deep neural network. This network is able to learn simultaneously a sparse representation of data in the time-frequency domain and a non-linear function that maps this representation into masks that decompose input data into a signal of interest and noise (defined as any non-seismic signal). We show that DeepDenoiser achieves impressive denoising of seismic signals even when the signal and noise share a common frequency band. Our method properly handles a variety of colored noise and non-earthquake signals. DeepDenoiser can significantly improve the SNR with minimal changes in the waveform shape of interest, even in presence of high noise levels. We demonstrate the effect of our method on improving earthquake detection. There are clear applications of DeepDenoiser to seismic imaging, micro-seismic monitoring, and preprocessing of ambient noise data. We also note that potential applications of our approach are not limited to these applications or even to earthquake data, and that our approach can be adapted to diverse signals and applications in other settings.

Deep neural networks have shown promise for music audio signal processing applications, often surpassing prior approaches, particularly as end-to-end models in the waveform domain. Yet results to date have tended to be constrained by low sample rates, noise, narrow domains of signal types, and/or lack of parameterized controls (i.e. "knobs"), making their suitability for professional audio engineering workflows still lacking. This work expands on prior research published on modeling nonlinear time-dependent signal processing effects associated with music production by means of a deep neural network, one which includes the ability to emulate the parameterized settings you would see on an analog piece of equipment, with the goal of eventually producing commercially viable, high quality audio, i.e. 44.1 kHz sampling rate at 16-bit resolution. The results in this paper highlight progress in modeling these effects through architecture and optimization changes, towards increasing computational efficiency, lowering signal-to-noise ratio, and extending to a larger variety of nonlinear audio effects. Toward these ends, the strategies employed involved a three-pronged approach: model speed, model accuracy, and model generalizability. Most of the presented methods provide marginal or no increase in output accuracy over the original model, with the exception of dataset manipulation. We found that limiting the audio content of the dataset, for example using datasets of just a single instrument, provided a significant improvement in model accuracy over models trained on more general datasets.

Diffusion models have gained traction as powerful algorithms for synthesizing high-quality images. Central to these algorithms is the diffusion process, a set of equations which maps data to noise in a way that can significantly affect performance. In this paper, we explore whether the diffusion process can be learned from data. Our work is grounded in Bayesian inference and seeks to improve log-likelihood estimation by casting the learned diffusion process as an approximate variational posterior that yields a tighter lower bound (ELBO) on the likelihood. A widely held assumption is that the ELBO is invariant to the noise process: our work dispels this assumption and proposes multivariate learned adaptive noise (MULAN), a learned diffusion process that applies noise at different rates across an image. Specifically, our method relies on a multivariate noise schedule that is a function of the data to ensure that the ELBO is no longer invariant to the choice of the noise schedule as in previous works. Empirically, MULAN sets a new state-of-the-art in density estimation on CIFAR-10 and ImageNet and reduces the number of training steps by 50%. Code is available at https://github.com/s-sahoo/MuLAN

Deep neural network is difficult to train and this predicament becomes worse as the depth increases. The essence of this problem exists in the magnitude of backpropagated errors that will result in gradient vanishing or exploding phenomenon. We show that a variant of regularizer which utilizes orthonormality among different filter banks can alleviate this problem. Moreover, we design a backward error modulation mechanism based on the quasi-isometry assumption between two consecutive parametric layers. Equipped with these two ingredients, we propose several novel optimization solutions that can be utilized for training a specific-structured (repetitively triple modules of Conv-BNReLU) extremely deep convolutional neural network (CNN) WITHOUT any shortcuts/ identity mappings from scratch. Experiments show that our proposed solutions can achieve distinct improvements for a 44-layer and a 110-layer plain networks on both the CIFAR-10 and ImageNet datasets. Moreover, we can successfully train plain CNNs to match the performance of the residual counterparts. Besides, we propose new principles for designing network structure from the insights evoked by orthonormality. Combined with residual structure, we achieve comparative performance on the ImageNet dataset.

We propose the Fourier Adaptive Lite Diffusion Architecture (FALDA), a novel probabilistic framework for time series forecasting. First, we introduce the Diffusion Model for Residual Regression (DMRR) framework, which unifies diffusion-based probabilistic regression methods. Within this framework, FALDA leverages Fourier-based decomposition to incorporate a component-specific architecture, enabling tailored modeling of individual temporal components. A conditional diffusion model is utilized to estimate the future noise term, while our proposed lightweight denoiser, DEMA (Decomposition MLP with AdaLN), conditions on the historical noise term to enhance denoising performance. Through mathematical analysis and empirical validation, we demonstrate that FALDA effectively reduces epistemic uncertainty, allowing probabilistic learning to primarily focus on aleatoric uncertainty. Experiments on six real-world benchmarks demonstrate that FALDA consistently outperforms existing probabilistic forecasting approaches across most datasets for long-term time series forecasting while achieving enhanced computational efficiency without compromising accuracy. Notably, FALDA also achieves superior overall performance compared to state-of-the-art (SOTA) point forecasting approaches, with improvements of up to 9%.

In speech enhancement and source separation, signal-to-noise ratio is a ubiquitous objective measure of denoising/separation quality. A decade ago, the BSS_eval toolkit was developed to give researchers worldwide a way to evaluate the quality of their algorithms in a simple, fair, and hopefully insightful way: it attempted to account for channel variations, and to not only evaluate the total distortion in the estimated signal but also split it in terms of various factors such as remaining interference, newly added artifacts, and channel errors. In recent years, hundreds of papers have been relying on this toolkit to evaluate their proposed methods and compare them to previous works, often arguing that differences on the order of 0.1 dB proved the effectiveness of a method over others. We argue here that the signal-to-distortion ratio (SDR) implemented in the BSS_eval toolkit has generally been improperly used and abused, especially in the case of single-channel separation, resulting in misleading results. We propose to use a slightly modified definition, resulting in a simpler, more robust measure, called scale-invariant SDR (SI-SDR). We present various examples of critical failure of the original SDR that SI-SDR overcomes.

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also discuss connections with other methods such as score-based diffusion models, stochastic localization processes, probabilistic denoising techniques, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.

This paper proposes a generative speech enhancement model based on Schr\"odinger bridge (SB). The proposed model is employing a tractable SB to formulate a data-to-data process between the clean speech distribution and the observed noisy speech distribution. The model is trained with a data prediction loss, aiming to recover the complex-valued clean speech coefficients, and an auxiliary time-domain loss is used to improve training of the model. The effectiveness of the proposed SB-based model is evaluated in two different speech enhancement tasks: speech denoising and speech dereverberation. The experimental results demonstrate that the proposed SB-based outperforms diffusion-based models in terms of speech quality metrics and ASR performance, e.g., resulting in relative word error rate reduction of 20% for denoising and 6% for dereverberation compared to the best baseline model. The proposed model also demonstrates improved efficiency, achieving better quality than the baselines for the same number of sampling steps and with a reduced computational cost.

Satellite remote sensing missions have gained popularity over the past fifteen years due to their ability to cover large swaths of land at regular intervals, making them ideal for monitoring environmental trends. The FINCH mission, a 3U+ CubeSat equipped with a hyperspectral camera, aims to monitor crop residue cover in agricultural fields. Although hyperspectral imaging captures both spectral and spatial information, it is prone to various types of noise, including random noise, stripe noise, and dead pixels. Effective denoising of these images is crucial for downstream scientific tasks. Traditional methods, including hand-crafted techniques encoding strong priors, learned 2D image denoising methods applied across different hyperspectral bands, or diffusion generative models applied independently on bands, often struggle with varying noise strengths across spectral bands, leading to significant spectral distortion. This paper presents a novel approach to hyperspectral image denoising using latent diffusion models that integrate spatial and spectral information. We particularly do so by building a 3D diffusion model and presenting a 3-stage training approach on real and synthetically crafted datasets. The proposed method preserves image structure while reducing noise. Evaluations on both popular hyperspectral denoising datasets and synthetically crafted datasets for the FINCH mission demonstrate the effectiveness of this approach.

Because diffusion models have shown impressive performances in a number of tasks, such as image synthesis, there is a trend in recent works to prove (with certain assumptions) that these models have strong approximation capabilities. In this paper, we show that current diffusion models actually have an expressive bottleneck in backward denoising and some assumption made by existing theoretical guarantees is too strong. Based on this finding, we prove that diffusion models have unbounded errors in both local and global denoising. In light of our theoretical studies, we introduce soft mixture denoising (SMD), an expressive and efficient model for backward denoising. SMD not only permits diffusion models to well approximate any Gaussian mixture distributions in theory, but also is simple and efficient for implementation. Our experiments on multiple image datasets show that SMD significantly improves different types of diffusion models (e.g., DDPM), espeically in the situation of few backward iterations.

We investigate the expressive power of depth-2 bandlimited random neural networks. A random net is a neural network where the hidden layer parameters are frozen with random assignment, and only the output layer parameters are trained by loss minimization. Using random weights for a hidden layer is an effective method to avoid non-convex optimization in standard gradient descent learning. It has also been adopted in recent deep learning theories. Despite the well-known fact that a neural network is a universal approximator, in this study, we mathematically show that when hidden parameters are distributed in a bounded domain, the network may not achieve zero approximation error. In particular, we derive a new nontrivial approximation error lower bound. The proof utilizes the technique of ridgelet analysis, a harmonic analysis method designed for neural networks. This method is inspired by fundamental principles in classical signal processing, specifically the idea that signals with limited bandwidth may not always be able to perfectly recreate the original signal. We corroborate our theoretical results with various simulation studies, and generally, two main take-home messages are offered: (i) Not any distribution for selecting random weights is feasible to build a universal approximator; (ii) A suitable assignment of random weights exists but to some degree is associated with the complexity of the target function.

Diffusion-based generative models have recently gained attention in speech enhancement (SE), providing an alternative to conventional supervised methods. These models transform clean speech training samples into Gaussian noise centered at noisy speech, and subsequently learn a parameterized model to reverse this process, conditionally on noisy speech. Unlike supervised methods, generative-based SE approaches usually rely solely on an unsupervised loss, which may result in less efficient incorporation of conditioned noisy speech. To address this issue, we propose augmenting the original diffusion training objective with a mean squared error (MSE) loss, measuring the discrepancy between estimated enhanced speech and ground-truth clean speech at each reverse process iteration. Experimental results demonstrate the effectiveness of our proposed methodology.

We present a neural network architecture designed to naturally learn a positional embedding and overcome the spectral bias towards lower frequencies faced by conventional implicit neural representation networks. Our proposed architecture, SPDER, is a simple MLP that uses an activation function composed of a sinusoidal multiplied by a sublinear function, called the damping function. The sinusoidal enables the network to automatically learn the positional embedding of an input coordinate while the damping passes on the actual coordinate value by preventing it from being projected down to within a finite range of values. Our results indicate that SPDERs speed up training by 10x and converge to losses 1,500-50,000x lower than that of the state-of-the-art for image representation. SPDER is also state-of-the-art in audio representation. The superior representation capability allows SPDER to also excel on multiple downstream tasks such as image super-resolution and video frame interpolation. We provide intuition as to why SPDER significantly improves fitting compared to that of other INR methods while requiring no hyperparameter tuning or preprocessing.

In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees on the quality of approximation, while reducing the number of examples to the product of the VC dimension d and the total sensitivity mathfrak S in remarkably general settings. However, guarantees going beyond this general bound of mathfrak S d are known in perhaps only one setting, for ell_2 subspace embeddings, despite intense study of sensitivity sampling in prior work. In this work, we show the first bounds for sensitivity sampling for ell_p subspace embeddings for pneq 2 that improve over the general mathfrak S d bound, achieving a bound of roughly mathfrak S^{2/p} for 1leq p<2 and mathfrak S^{2-2/p} for 2<p<infty. For 1leq p<2, we show that this bound is tight, in the sense that there exist matrices for which mathfrak S^{2/p} samples is necessary. Furthermore, our techniques yield further new results in the study of sampling algorithms, showing that the root leverage score sampling algorithm achieves a bound of roughly d for 1leq p<2, and that a combination of leverage score and sensitivity sampling achieves an improved bound of roughly d^{2/p}mathfrak S^{2-4/p} for 2<p<infty. Our sensitivity sampling results yield the best known sample complexity for a wide class of structured matrices that have small ell_p sensitivity.

There are several applications of stochastic optimization where one can benefit from a robust estimate of the gradient. For example, domains such as distributed learning with corrupted nodes, the presence of large outliers in the training data, learning under privacy constraints, or even heavy-tailed noise due to the dynamics of the algorithm itself. Here we study SGD with robust gradient estimators based on estimating the median. We first consider computing the median gradient across samples, and show that the resulting method can converge even under heavy-tailed, state-dependent noise. We then derive iterative methods based on the stochastic proximal point method for computing the geometric median and generalizations thereof. Finally we propose an algorithm estimating the median gradient across iterations, and find that several well known methods - in particular different forms of clipping - are particular cases of this framework.

The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to random variables are discussed, including the approach based on completions in a Polish space. We apply the theory to the study of stochastic dynamical systems in discrete-time, and give a brief exposition of the Wiener process as a foundation for stochastic differential equations. The theory is based within the framework of type-two effectivity, so has an explicit direct link with Turing computation, and is expressed in a system of computable types and operations, so has a clean mathematical description.

A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally tractable. Here, we develop an approach that simultaneously achieves both flexibility and tractability. The essential idea, inspired by non-equilibrium statistical physics, is to systematically and slowly destroy structure in a data distribution through an iterative forward diffusion process. We then learn a reverse diffusion process that restores structure in data, yielding a highly flexible and tractable generative model of the data. This approach allows us to rapidly learn, sample from, and evaluate probabilities in deep generative models with thousands of layers or time steps, as well as to compute conditional and posterior probabilities under the learned model. We additionally release an open source reference implementation of the algorithm.

Reasoning from sequences of raw sensory data is a ubiquitous problem across fields ranging from medical devices to robotics. These problems often involve using long sequences of raw sensor data (e.g. magnetometers, piezoresistors) to predict sequences of desirable physical quantities (e.g. force, inertial measurements). While classical approaches are powerful for locally-linear prediction problems, they often fall short when using real-world sensors. These sensors are typically non-linear, are affected by extraneous variables (e.g. vibration), and exhibit data-dependent drift. For many problems, the prediction task is exacerbated by small labeled datasets since obtaining ground-truth labels requires expensive equipment. In this work, we present Hierarchical State-Space Models (HiSS), a conceptually simple, new technique for continuous sequential prediction. HiSS stacks structured state-space models on top of each other to create a temporal hierarchy. Across six real-world sensor datasets, from tactile-based state prediction to accelerometer-based inertial measurement, HiSS outperforms state-of-the-art sequence models such as causal Transformers, LSTMs, S4, and Mamba by at least 23% on MSE. Our experiments further indicate that HiSS demonstrates efficient scaling to smaller datasets and is compatible with existing data-filtering techniques. Code, datasets and videos can be found on https://hiss-csp.github.io.

The analysis of parametric and non-parametric uncertainties of very large dynamical systems requires the construction of a stochastic model of said system. Linear approaches relying on random matrix theory and principal componant analysis can be used when systems undergo low-frequency vibrations. In the case of fast dynamics and wave propagation, we investigate a random generator of boundary conditions for fast submodels by using machine learning. We show that the use of non-linear techniques in machine learning and data-driven methods is highly relevant. Physics-informed neural networks is a possible choice for a data-driven method to replace linear modal analysis. An architecture that support a random component is necessary for the construction of the stochastic model of the physical system for non-parametric uncertainties, since the goal is to learn the underlying probabilistic distribution of uncertainty in the data. Generative Adversarial Networks (GANs) are suited for such applications, where the Wasserstein-GAN with gradient penalty variant offers improved convergence results for our problem. The objective of our approach is to train a GAN on data from a finite element method code (Fenics) so as to extract stochastic boundary conditions for faster finite element predictions on a submodel. The submodel and the training data have both the same geometrical support. It is a zone of interest for uncertainty quantification and relevant to engineering purposes. In the exploitation phase, the framework can be viewed as a randomized and parametrized simulation generator on the submodel, which can be used as a Monte Carlo estimator.

The lack of clean speech is a practical challenge to the development of speech enhancement systems, which means that there is an inevitable mismatch between their training criterion and evaluation metric. In response to this unfavorable situation, we propose a training and inference strategy that additionally uses enhanced speech as a target by improving the previously proposed noisy-target training (NyTT). Because homogeneity between in-domain noise and extraneous noise is the key to the effectiveness of NyTT, we train various student models by remixing 1) the teacher model's estimated speech and noise for enhanced-target training or 2) raw noisy speech and the teacher model's estimated noise for noisy-target training. Experimental results show that our proposed method outperforms several baselines, especially with the teacher/student inference, where predicted clean speech is derived successively through the teacher and final student models.

This study presents a new image super-resolution (SR) technique based on diffusion inversion, aiming at harnessing the rich image priors encapsulated in large pre-trained diffusion models to improve SR performance. We design a Partial noise Prediction strategy to construct an intermediate state of the diffusion model, which serves as the starting sampling point. Central to our approach is a deep noise predictor to estimate the optimal noise maps for the forward diffusion process. Once trained, this noise predictor can be used to initialize the sampling process partially along the diffusion trajectory, generating the desirable high-resolution result. Compared to existing approaches, our method offers a flexible and efficient sampling mechanism that supports an arbitrary number of sampling steps, ranging from one to five. Even with a single sampling step, our method demonstrates superior or comparable performance to recent state-of-the-art approaches. The code and model are publicly available at https://github.com/zsyOAOA/InvSR.

Recently, deep neural networks such as RNN, CNN and Transformer have been applied in the task of sequential recommendation, which aims to capture the dynamic preference characteristics from logged user behavior data for accurate recommendation. However, in online platforms, logged user behavior data is inevitable to contain noise, and deep recommendation models are easy to overfit on these logged data. To tackle this problem, we borrow the idea of filtering algorithms from signal processing that attenuates the noise in the frequency domain. In our empirical experiments, we find that filtering algorithms can substantially improve representative sequential recommendation models, and integrating simple filtering algorithms (eg Band-Stop Filter) with an all-MLP architecture can even outperform competitive Transformer-based models. Motivated by it, we propose FMLP-Rec, an all-MLP model with learnable filters for sequential recommendation task. The all-MLP architecture endows our model with lower time complexity, and the learnable filters can adaptively attenuate the noise information in the frequency domain. Extensive experiments conducted on eight real-world datasets demonstrate the superiority of our proposed method over competitive RNN, CNN, GNN and Transformer-based methods. Our code and data are publicly available at the link: blue{https://github.com/RUCAIBox/FMLP-Rec}.

Denoisers play a central role in many applications, from noise suppression in low-grade imaging sensors, to empowering score-based generative models. The latter category of methods makes use of Tweedie's formula, which links the posterior mean in Gaussian denoising (\ie the minimum MSE denoiser) with the score of the data distribution. Here, we derive a fundamental relation between the higher-order central moments of the posterior distribution, and the higher-order derivatives of the posterior mean. We harness this result for uncertainty quantification of pre-trained denoisers. Particularly, we show how to efficiently compute the principal components of the posterior distribution for any desired region of an image, as well as to approximate the full marginal distribution along those (or any other) one-dimensional directions. Our method is fast and memory-efficient, as it does not explicitly compute or store the high-order moment tensors and it requires no training or fine tuning of the denoiser. Code and examples are available on the project webpage in https://hilamanor.github.io/GaussianDenoisingPosterior/ .

There have been many image denoisers using deep neural networks, which outperform conventional model-based methods by large margins. Recently, self-supervised methods have attracted attention because constructing a large real noise dataset for supervised training is an enormous burden. The most representative self-supervised denoisers are based on blind-spot networks, which exclude the receptive field's center pixel. However, excluding any input pixel is abandoning some information, especially when the input pixel at the corresponding output position is excluded. In addition, a standard blind-spot network fails to reduce real camera noise due to the pixel-wise correlation of noise, though it successfully removes independently distributed synthetic noise. Hence, to realize a more practical denoiser, we propose a novel self-supervised training framework that can remove real noise. For this, we derive the theoretic upper bound of a supervised loss where the network is guided by the downsampled blinded output. Also, we design a conditional blind-spot network (C-BSN), which selectively controls the blindness of the network to use the center pixel information. Furthermore, we exploit a random subsampler to decorrelate noise spatially, making the C-BSN free of visual artifacts that were often seen in downsample-based methods. Extensive experiments show that the proposed C-BSN achieves state-of-the-art performance on real-world datasets as a self-supervised denoiser and shows qualitatively pleasing results without any post-processing or refinement.

We present a new methodology for detecting out-of-distribution (OOD) images by utilizing norms of the score estimates at multiple noise scales. A score is defined to be the gradient of the log density with respect to the input data. Our methodology is completely unsupervised and follows a straight forward training scheme. First, we train a deep network to estimate scores for levels of noise. Once trained, we calculate the noisy score estimates for N in-distribution samples and take the L2-norms across the input dimensions (resulting in an NxL matrix). Then we train an auxiliary model (such as a Gaussian Mixture Model) to learn the in-distribution spatial regions in this L-dimensional space. This auxiliary model can now be used to identify points that reside outside the learned space. Despite its simplicity, our experiments show that this methodology significantly outperforms the state-of-the-art in detecting out-of-distribution images. For example, our method can effectively separate CIFAR-10 (inlier) and SVHN (OOD) images, a setting which has been previously shown to be difficult for deep likelihood models.

In this work, we build a simple but strong baseline for sounding video generation. Given base diffusion models for audio and video, we integrate them with additional modules into a single model and train it to make the model jointly generate audio and video. To enhance alignment between audio-video pairs, we introduce two novel mechanisms in our model. The first one is timestep adjustment, which provides different timestep information to each base model. It is designed to align how samples are generated along with timesteps across modalities. The second one is a new design of the additional modules, termed Cross-Modal Conditioning as Positional Encoding (CMC-PE). In CMC-PE, cross-modal information is embedded as if it represents temporal position information, and the embeddings are fed into the model like positional encoding. Compared with the popular cross-attention mechanism, CMC-PE provides a better inductive bias for temporal alignment in the generated data. Experimental results validate the effectiveness of the two newly introduced mechanisms and also demonstrate that our method outperforms existing methods.

Although diffusion models (DMs) have shown promising performances in a number of tasks (e.g., speech synthesis and image generation), they might suffer from error propagation because of their sequential structure. However, this is not certain because some sequential models, such as Conditional Random Field (CRF), are free from this problem. To address this issue, we develop a theoretical framework to mathematically formulate error propagation in the architecture of DMs, The framework contains three elements, including modular error, cumulative error, and propagation equation. The modular and cumulative errors are related by the equation, which interprets that DMs are indeed affected by error propagation. Our theoretical study also suggests that the cumulative error is closely related to the generation quality of DMs. Based on this finding, we apply the cumulative error as a regularization term to reduce error propagation. Because the term is computationally intractable, we derive its upper bound and design a bootstrap algorithm to efficiently estimate the bound for optimization. We have conducted extensive experiments on multiple image datasets, showing that our proposed regularization reduces error propagation, significantly improves vanilla DMs, and outperforms previous baselines.

The capability of video super-resolution (VSR) to synthesize high-resolution (HR) video from ideal datasets has been demonstrated in many works. However, applying the VSR model to real-world video with unknown and complex degradation remains a challenging task. First, existing degradation metrics in most VSR methods are not able to effectively simulate real-world noise and blur. On the contrary, simple combinations of classical degradation are used for real-world noise modeling, which led to the VSR model often being violated by out-of-distribution noise. Second, many SR models focus on noise simulation and transfer. Nevertheless, the sampled noise is monotonous and limited. To address the aforementioned problems, we propose a Negatives augmentation strategy for generalized noise modeling in Video Super-Resolution (NegVSR) task. Specifically, we first propose sequential noise generation toward real-world data to extract practical noise sequences. Then, the degeneration domain is widely expanded by negative augmentation to build up various yet challenging real-world noise sets. We further propose the augmented negative guidance loss to learn robust features among augmented negatives effectively. Extensive experiments on real-world datasets (e.g., VideoLQ and FLIR) show that our method outperforms state-of-the-art methods with clear margins, especially in visual quality.

Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values due to reasons including: erroneous sensors, data entry/processing mistakes, or imperfect human estimates. We consider general regression settings with covariates and a potentially corrupted response whose observed values may contain errors. By accounting for various uncertainties, we introduced veracity scores that distinguish between genuine errors and natural data fluctuations, conditioned on the available covariate information in the dataset. We propose a simple yet efficient filtering procedure for eliminating potential errors, and establish theoretical guarantees for our method. We also contribute a new error detection benchmark involving 5 regression datasets with real-world numerical errors (for which the true values are also known). In this benchmark and additional simulation studies, our method identifies incorrect values with better precision/recall than other approaches.

With the rapid deployment of SCADA systems, how to effectively analyze industrial signals and detect abnormal states is an urgent need for the industry. Due to the significant heterogeneity of these signals, which we summarize as the M5 problem, previous works only focus on small sub-problems and employ specialized models, failing to utilize the synergies between modalities and the powerful scaling law. However, we argue that the M5 signals can be modeled in a unified manner due to the intrinsic similarity. As a result, we propose FISHER, a Foundation model for multi-modal Industrial Signal compreHEnsive Representation. To support arbitrary sampling rates, FISHER considers the increment of sampling rate as the concatenation of sub-band information. Specifically, FISHER takes the STFT sub-band as the modeling unit and adopts a teacher student SSL framework for pre-training. We also develop the RMIS benchmark, which evaluates the representations of M5 industrial signals on multiple health management tasks. Compared with top SSL models, FISHER showcases versatile and outstanding capabilities with a general performance gain up to 5.03%, along with much more efficient scaling curves. We also investigate the scaling law on downstream tasks and derive potential avenues for future works. FISHER is now open-sourced on https://github.com/jianganbai/FISHER

Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and multi-scale PDEs, which can be due to spectral bias during neural network training. To address this problem, we resort to the Gaussian process (GP) framework. To flexibly capture the dominant frequencies, we model the power spectrum of the PDE solution with a student t mixture or Gaussian mixture. We apply the inverse Fourier transform to obtain the covariance function (by Wiener-Khinchin theorem). The covariance derived from the Gaussian mixture spectrum corresponds to the known spectral mixture kernel. Next, we estimate the mixture weights in the log domain, which we show is equivalent to placing a Jeffreys prior. It automatically induces sparsity, prunes excessive frequencies, and adjusts the remaining toward the ground truth. Third, to enable efficient and scalable computation on massive collocation points, which are critical to capture high frequencies, we place the collocation points on a grid, and multiply our covariance function at each input dimension. We use the GP conditional mean to predict the solution and its derivatives so as to fit the boundary condition and the equation itself. As a result, we can derive a Kronecker product structure in the covariance matrix. We use Kronecker product properties and multilinear algebra to promote computational efficiency and scalability, without low-rank approximations. We show the advantage of our method in systematic experiments. The code is released at https://github.com/xuangu-fang/Gaussian-Process-Slover-for-High-Freq-PDE.

Soundscape augmentation is an emerging approach for noise mitigation by introducing additional sounds known as "maskers" to increase acoustic comfort. Traditionally, the choice of maskers is often predicated on expert guidance or post-hoc analysis which can be time-consuming and sometimes arbitrary. Moreover, this often results in a static set of maskers that are inflexible to the dynamic nature of real-world acoustic environments. Overcoming the inflexibility of traditional soundscape augmentation is twofold. First, given a snapshot of a soundscape, the system must be able to select an optimal masker without human supervision. Second, the system must also be able to react to changes in the acoustic environment with near real-time latency. In this work, we harness the combined prowess of cloud computing and the Internet of Things (IoT) to allow in-situ listening and playback using microcontrollers while delegating computationally expensive inference tasks to the cloud. In particular, a serverless cloud architecture was used for inference, ensuring near real-time latency and scalability without the need to provision computing resources. A working prototype of the system is currently being deployed in a public area experiencing high traffic noise, as well as undergoing public evaluation for future improvements.

A collection of robust Mahalanobis distances for multivariate outlier detection is proposed, based on the notion of shrinkage. Robust intensity and scaling factors are optimally estimated to define the shrinkage. Some properties are investigated, such as affine equivariance and breakdown value. The performance of the proposal is illustrated through the comparison to other techniques from the literature, in a simulation study and with a real dataset. The behavior when the underlying distribution is heavy-tailed or skewed, shows the appropriateness of the method when we deviate from the common assumption of normality. The resulting high correct detection rates and low false detection rates in the vast majority of cases, as well as the significantly smaller computation time shows the advantages of our proposal.

We examine the geometry of neural network training using the Jacobian of trained network parameters with respect to their initial values. Our analysis reveals low-dimensional structure in the training process which is dependent on the input data but largely independent of the labels. We find that the singular value spectrum of the Jacobian matrix consists of three distinctive regions: a "chaotic" region of values orders of magnitude greater than one, a large "bulk" region of values extremely close to one, and a "stable" region of values less than one. Along each bulk direction, the left and right singular vectors are nearly identical, indicating that perturbations to the initialization are carried through training almost unchanged. These perturbations have virtually no effect on the network's output in-distribution, yet do have an effect far out-of-distribution. While the Jacobian applies only locally around a single initialization, we find substantial overlap in bulk subspaces for different random seeds. Our code is available at https://github.com/EleutherAI/training-jacobian

In this paper, we focus on Whisper, a recent automatic speech recognition model trained with a massive 680k hour labeled speech corpus recorded in diverse conditions. We first show an interesting finding that while Whisper is very robust against real-world background sounds (e.g., music), its audio representation is actually not noise-invariant, but is instead highly correlated to non-speech sounds, indicating that Whisper recognizes speech conditioned on the noise type. With this finding, we build a unified audio tagging and speech recognition model Whisper-AT by freezing the backbone of Whisper, and training a lightweight audio tagging model on top of it. With <1% extra computational cost, Whisper-AT can recognize audio events, in addition to spoken text, in a single forward pass.

In this paper, we propose a vocoder based on a pair of forward and reverse-time linear stochastic differential equations (SDE). The solutions of this SDE pair are two stochastic processes, one of which turns the distribution of wave, that we want to generate, into a simple and tractable distribution. The other is the generation procedure that turns this tractable simple signal into the target wave. The model is called It\^oWave. It\^oWave use the Wiener process as a driver to gradually subtract the excess signal from the noise signal to generate realistic corresponding meaningful audio respectively, under the conditional inputs of original mel spectrogram. The results of the experiment show that the mean opinion scores (MOS) of It\^oWave can exceed the current state-of-the-art (SOTA) methods, and reached 4.35pm0.115. The generated audio samples are available online.

We introduce an algorithm where the individual bits representing the weights of a neural network are learned. This method allows training weights with integer values on arbitrary bit-depths and naturally uncovers sparse networks, without additional constraints or regularization techniques. We show better results than the standard training technique with fully connected networks and similar performance as compared to standard training for convolutional and residual networks. By training bits in a selective manner we found that the biggest contribution to achieving high accuracy is given by the first three most significant bits, while the rest provide an intrinsic regularization. As a consequence more than 90\% of a network can be used to store arbitrary codes without affecting its accuracy. These codes may be random noise, binary files or even the weights of previously trained networks.

Sparse coding, which refers to modeling a signal as sparse linear combinations of the elements of a learned dictionary, has proven to be a successful (and interpretable) approach in applications such as signal processing, computer vision, and medical imaging. While this success has spurred much work on provable guarantees for dictionary recovery when the learned dictionary is the same size as the ground-truth dictionary, work on the setting where the learned dictionary is larger (or over-realized) with respect to the ground truth is comparatively nascent. Existing theoretical results in this setting have been constrained to the case of noise-less data. We show in this work that, in the presence of noise, minimizing the standard dictionary learning objective can fail to recover the elements of the ground-truth dictionary in the over-realized regime, regardless of the magnitude of the signal in the data-generating process. Furthermore, drawing from the growing body of work on self-supervised learning, we propose a novel masking objective for which recovering the ground-truth dictionary is in fact optimal as the signal increases for a large class of data-generating processes. We corroborate our theoretical results with experiments across several parameter regimes showing that our proposed objective also enjoys better empirical performance than the standard reconstruction objective.

Deep learning has achieved remarkable success in graph-related tasks, yet this accomplishment heavily relies on large-scale high-quality annotated datasets. However, acquiring such datasets can be cost-prohibitive, leading to the practical use of labels obtained from economically efficient sources such as web searches and user tags. Unfortunately, these labels often come with noise, compromising the generalization performance of deep networks. To tackle this challenge and enhance the robustness of deep learning models against label noise in graph-based tasks, we propose a method called ERASE (Error-Resilient representation learning on graphs for lAbel noiSe tolerancE). The core idea of ERASE is to learn representations with error tolerance by maximizing coding rate reduction. Particularly, we introduce a decoupled label propagation method for learning representations. Before training, noisy labels are pre-corrected through structural denoising. During training, ERASE combines prototype pseudo-labels with propagated denoised labels and updates representations with error resilience, which significantly improves the generalization performance in node classification. The proposed method allows us to more effectively withstand errors caused by mislabeled nodes, thereby strengthening the robustness of deep networks in handling noisy graph data. Extensive experimental results show that our method can outperform multiple baselines with clear margins in broad noise levels and enjoy great scalability. Codes are released at https://github.com/eraseai/erase.

Recent years have seen progress beyond domain-specific sound separation for speech or music towards universal sound separation for arbitrary sounds. Prior work on universal sound separation has investigated separating a target sound out of an audio mixture given a text query. Such text-queried sound separation systems provide a natural and scalable interface for specifying arbitrary target sounds. However, supervised text-queried sound separation systems require costly labeled audio-text pairs for training. Moreover, the audio provided in existing datasets is often recorded in a controlled environment, causing a considerable generalization gap to noisy audio in the wild. In this work, we aim to approach text-queried universal sound separation by using only unlabeled data. We propose to leverage the visual modality as a bridge to learn the desired audio-textual correspondence. The proposed CLIPSep model first encodes the input query into a query vector using the contrastive language-image pretraining (CLIP) model, and the query vector is then used to condition an audio separation model to separate out the target sound. While the model is trained on image-audio pairs extracted from unlabeled videos, at test time we can instead query the model with text inputs in a zero-shot setting, thanks to the joint language-image embedding learned by the CLIP model. Further, videos in the wild often contain off-screen sounds and background noise that may hinder the model from learning the desired audio-textual correspondence. To address this problem, we further propose an approach called noise invariant training for training a query-based sound separation model on noisy data. Experimental results show that the proposed models successfully learn text-queried universal sound separation using only noisy unlabeled videos, even achieving competitive performance against a supervised model in some settings.

Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the choice of image degradation, and in fact an entire family of generative models can be constructed by varying this choice. Even when using completely deterministic degradations (e.g., blur, masking, and more), the training and test-time update rules that underlie diffusion models can be easily generalized to create generative models. The success of these fully deterministic models calls into question the community's understanding of diffusion models, which relies on noise in either gradient Langevin dynamics or variational inference, and paves the way for generalized diffusion models that invert arbitrary processes. Our code is available at https://github.com/arpitbansal297/Cold-Diffusion-Models

We introduce Audio-SDS, a generalization of Score Distillation Sampling (SDS) to text-conditioned audio diffusion models. While SDS was initially designed for text-to-3D generation using image diffusion, its core idea of distilling a powerful generative prior into a separate parametric representation extends to the audio domain. Leveraging a single pretrained model, Audio-SDS enables a broad range of tasks without requiring specialized datasets. In particular, we demonstrate how Audio-SDS can guide physically informed impact sound simulations, calibrate FM-synthesis parameters, and perform prompt-specified source separation. Our findings illustrate the versatility of distillation-based methods across modalities and establish a robust foundation for future work using generative priors in audio tasks.

In this paper, we work on a sound recognition system that continually incorporates new sound classes. Our main goal is to develop a framework where the model can be updated without relying on labeled data. For this purpose, we propose adopting representation learning, where an encoder is trained using unlabeled data. This learning framework enables the study and implementation of a practically relevant use case where only a small amount of the labels is available in a continual learning context. We also make the empirical observation that a similarity-based representation learning method within this framework is robust to forgetting even if no explicit mechanism against forgetting is employed. We show that this approach obtains similar performance compared to several distillation-based continual learning methods when employed on self-supervised representation learning methods.

The goal of this paper is to generate realistic audio with a lightweight and fast diffusion-based vocoder, named FreGrad. Our framework consists of the following three key components: (1) We employ discrete wavelet transform that decomposes a complicated waveform into sub-band wavelets, which helps FreGrad to operate on a simple and concise feature space, (2) We design a frequency-aware dilated convolution that elevates frequency awareness, resulting in generating speech with accurate frequency information, and (3) We introduce a bag of tricks that boosts the generation quality of the proposed model. In our experiments, FreGrad achieves 3.7 times faster training time and 2.2 times faster inference speed compared to our baseline while reducing the model size by 0.6 times (only 1.78M parameters) without sacrificing the output quality. Audio samples are available at: https://mm.kaist.ac.kr/projects/FreGrad.

In this work we present a data-driven approach for predicting the behavior of (i.e., profiling) a given non-linear audio signal processing effect (henceforth "audio effect"). Our objective is to learn a mapping function that maps the unprocessed audio to the processed by the audio effect to be profiled, using time-domain samples. To that aim, we employ a deep auto-encoder model that is conditioned on both time-domain samples and the control parameters of the target audio effect. As a test-case study, we focus on the offline profiling of two dynamic range compression audio effects, one software-based and the other analog. Compressors were chosen because they are a widely used and important set of effects and because their parameterized nonlinear time-dependent nature makes them a challenging problem for a system aiming to profile "general" audio effects. Results from our experimental procedure show that the primary functional and auditory characteristics of the compressors can be captured, however there is still sufficient audible noise to merit further investigation before such methods are applied to real-world audio processing workflows.