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Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…

Machine Learning · Statistics 2023-06-12 Aaron Lou , Stefano Ermon

Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…

Machine Learning · Statistics 2025-02-11 Alessandro Micheli , Mélodie Monod , Samir Bhatt

Distributed signal processing has attracted widespread attention in the scientific community due to its several advantages over centralized approaches. Recently, graph signal processing has risen to prominence, and adaptive distributed…

Signal Processing · Electrical Eng. & Systems 2020-08-07 Daniel G. Tiglea , Renato Candido , Magno T. M. Silva

Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality.…

Machine Learning · Computer Science 2023-03-06 Raghav Singhal , Mark Goldstein , Rajesh Ranganath

Diffusion models have shown remarkable potential in planning and control tasks due to their ability to represent multimodal distributions over actions and trajectories. However, ensuring safety under constraints remains a critical challenge…

Systems and Control · Electrical Eng. & Systems 2025-06-17 Jichen Zhang , Liqun Zhao , Antonis Papachristodoulou , Jack Umenberger

We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching…

Machine Learning · Statistics 2024-03-14 Xunpeng Huang , Hanze Dong , Yifan Hao , Yi-An Ma , Tong Zhang

Diffusion models have demonstrated impressive capabilities in synthesizing diverse content. However, despite their high-quality outputs, these models often perpetuate social biases, including those related to gender and race. These biases…

Computer Vision and Pattern Recognition · Computer Science 2025-03-27 Yingdong Shi , Changming Li , Yifan Wang , Yongxiang Zhao , Anqi Pang , Sibei Yang , Jingyi Yu , Kan Ren

Training a diffusion model approximates a map from a data distribution $\rho$ to the optimal score function $s_t$ for that distribution. Can we differentiate this map? If we could, then we could predict how the score, and ultimately the…

Machine Learning · Computer Science 2025-09-30 Christopher Scarvelis , Justin Solomon

Diffusion models have indeed shown great promise in solving inverse problems in image processing. In this paper, we propose a novel, problem-agnostic diffusion model called the maximum a posteriori (MAP)-based guided term estimation method…

Image and Video Processing · Electrical Eng. & Systems 2026-03-10 Pingping Tao , Haixia Liu , Jing Su

The Langevin algorithm is a classic method for sampling from a given pdf in a real space. In its basic version, it only requires knowledge of the gradient of the log-density, also called the score function. However, in deep learning, it is…

Machine Learning · Computer Science 2025-09-22 Aapo Hyvärinen

Graph diffusion models have gained significant attention in graph generation tasks, but they often inherit and amplify topology biases from sensitive attributes (e.g. gender, age, region), leading to unfair synthetic graphs. Existing fair…

Machine Learning · Computer Science 2026-03-03 Wendi Wang , Jiaxi Yang , Yongkang Du , Lu Lin

Generative AI models have recently achieved astonishing results in quality and are consequently employed in a fast-growing number of applications. However, since they are highly data-driven, relying on billion-sized datasets randomly…

Recently, a series of papers proposed deep learning-based approaches to sample from target distributions using controlled diffusion processes, being trained only on the unnormalized target densities without access to samples. Building on…

Machine Learning · Computer Science 2024-05-24 Lorenz Richter , Julius Berner

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

Methodology · Statistics 2018-02-14 Daniela Calvetti , Matthew M. Dunlop , Erkki Somersalo , Andrew M. Stuart

Purpose: The Unadjusted Langevin Algorithm (ULA) in combination with diffusion models can generate high quality MRI reconstructions with uncertainty estimation from highly undersampled k-space data. However, sampling methods such as…

Medical Physics · Physics 2026-05-26 Moritz Blumenthal , Tina Holliber , Jonathan I. Tamir , Martin Uecker

The recent, impressive advances in algorithmic generation of high-fidelity image, audio, and video are largely due to great successes in score-based diffusion models. A key implementing step is score matching, that is, the estimation of the…

Machine Learning · Statistics 2024-09-12 Zehao Dou , Subhodh Kotekal , Zhehao Xu , Harrison H. Zhou

Previous raw image-based low-light image enhancement methods predominantly relied on feed-forward neural networks to learn deterministic mappings from low-light to normally-exposed images. However, they failed to capture critical…

Computer Vision and Pattern Recognition · Computer Science 2023-08-16 Yufei Wang , Yi Yu , Wenhan Yang , Lanqing Guo , Lap-Pui Chau , Alex C. Kot , Bihan Wen

Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($\sigma \to 0$). In this work, we propose an alternative perspective: their success…

Machine Learning · Statistics 2026-03-17 Xiang Li , Zebang Shen , Ya-Ping Hsieh , Niao He

Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…

Machine Learning · Computer Science 2026-05-04 Saeed Mohseni-Sehdeh , Walid Saad , Kei Sakaguchi , Tao Yu

In supervised learning for image denoising, usually the paired clean images and noisy images are collected or synthesised to train a denoising model. L2 norm loss or other distance functions are used as the objective function for training.…

Computer Vision and Pattern Recognition · Computer Science 2023-02-07 Yutong Xie , Minne Yuan , Bin Dong , Quanzheng Li