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Inverse problems lie at the heart of modern imaging science, with broad applications in areas such as medical imaging, remote sensing, and microscopy. Recent years have witnessed a paradigm shift in solving imaging inverse problems, where…

Optimization and Control · Mathematics 2025-11-20 Hong Ye Tan , Subhadip Mukherjee , Junqi Tang

We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with…

Machine Learning · Computer Science 2021-07-02 Jay Whang , Qi Lei , Alexandros G. Dimakis

Recovering signals from low-order moments is a fundamental yet notoriously difficult task in inverse problems. This recovery process often reduces to solving ill-conditioned systems of polynomial equations. In this work, we propose a new…

Signal Processing · Electrical Eng. & Systems 2025-09-16 Rafi Beinhorn , Shay Kreymer , Amnon Balanov , Michael Cohen , Alon Zabatani , Tamir Bendory

Diffusion models have emerged as effective distribution estimators in vision, language, and reinforcement learning, but their use as priors in downstream tasks poses an intractable posterior inference problem. This paper studies amortized…

Generative diffusion models are becoming one of the most popular prior in image restoration (IR) tasks due to their remarkable ability to generate realistic natural images. Despite achieving satisfactory results, IR methods based on…

Computer Vision and Pattern Recognition · Computer Science 2025-01-27 Di You , Pier Luigi Dragotti

Diffusion models demonstrate remarkable capabilities in capturing complex data distributions and have achieved compelling results in many generative tasks. While they have recently been extended to dense prediction tasks such as depth…

Computer Vision and Pattern Recognition · Computer Science 2025-12-16 Haorui Ji , Taojun Lin , Hongdong Li

Diffusion models recently proved to be remarkable priors for Bayesian inverse problems. However, training these models typically requires access to large amounts of clean data, which could prove difficult in some settings. In this work, we…

Machine Learning · Computer Science 2025-11-04 François Rozet , Gérôme Andry , François Lanusse , Gilles Louppe

This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…

Machine Learning · Statistics 2026-02-12 Jean-François Giovannelli

Diffusion models have demonstrated remarkable efficacy in generating high-quality samples. Existing diffusion-based image restoration algorithms exploit pre-trained diffusion models to leverage data priors, yet they still preserve elements…

Image and Video Processing · Electrical Eng. & Systems 2024-08-07 Hongjie Wu , Linchao He , Mingqin Zhang , Dongdong Chen , Kunming Luo , Mengting Luo , Ji-Zhe Zhou , Hu Chen , Jiancheng Lv

Pretrained diffusion models have demonstrated strong capabilities in zero-shot inverse problem solving by incorporating observation information into the generation process of the diffusion models. However, this presents an inherent dilemma:…

Machine Learning · Computer Science 2026-05-05 Xun Su , Hiroyuki Kasai

Zero-shot image restoration (IR) methods based on pretrained diffusion models have recently achieved significant success. These methods typically require at least a parametric form of the degradation model. However, in real-world scenarios,…

Computer Vision and Pattern Recognition · Computer Science 2025-03-28 Hamadi Chihaoui , Paolo Favaro

This paper introduces UnDiff, a diffusion probabilistic model capable of solving various speech inverse tasks. Being once trained for speech waveform generation in an unconditional manner, it can be adapted to different tasks including…

Diffusion strategies have advanced visual motor control by progressively denoising high-dimensional action sequences, providing a promising method for robot manipulation. However, as task complexity increases, the success rate of existing…

Robotics · Computer Science 2026-01-21 Weize Xie , Yi Ding , Ying He , Leilei Wang , Binwen Bai , Zheyi Zhao , Chenyang Wang , F. Richard Yu

Imaging inverse problems are commonly addressed by minimizing measurement consistency and signal prior terms. While huge attention has been paid to developing high-performance priors, even the most advanced signal prior may lose its…

Image and Video Processing · Electrical Eng. & Systems 2026-05-19 Romario Gualdrón-Hurtado , Roman Jacome , Leon Suarez , Laura Galvis , Henry Arguello

Real-world image denoising is an extremely important image processing problem, which aims to recover clean images from noisy images captured in natural environments. In recent years, diffusion models have achieved very promising results in…

Computer Vision and Pattern Recognition · Computer Science 2023-05-09 Cheng Yang , Lijing Liang , Zhixun Su

Diffusion models have been increasingly used as strong generative priors for solving inverse problems such as super-resolution in medical imaging. However, these approaches typically utilize a diffusion prior trained at a single scale,…

Image and Video Processing · Electrical Eng. & Systems 2026-02-02 Darshan Thaker , Mahmoud Mostapha , Radu Miron , Shihan Qiu , Mariappan Nadar

In a great number of tasks in science and engineering, the goal is to infer an unknown image from a small number of measurements collected from a known forward model describing certain sensing or imaging modality. Due to resource…

Image and Video Processing · Electrical Eng. & Systems 2024-06-13 Xingyu Xu , Yuejie Chi

Inverse problems arise in a multitude of applications, where the goal is to recover a clean signal from noisy and possibly (non)linear observations. The difficulty of a reconstruction problem depends on multiple factors, such as the ground…

Image and Video Processing · Electrical Eng. & Systems 2024-08-21 Zalan Fabian , Berk Tinaz , Mahdi Soltanolkotabi

Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance.…

Image and Video Processing · Electrical Eng. & Systems 2022-03-22 Hyungjin Chung , Byeongsu Sim , Jong Chul Ye

Phase retrieval algorithms have become an important component in many modern computational imaging systems. For instance, in the context of ptychography and speckle correlation imaging, they enable imaging past the diffraction limit and…

Machine Learning · Statistics 2018-07-03 Christopher A. Metzler , Philip Schniter , Ashok Veeraraghavan , Richard G. Baraniuk