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Diffusion model-based inverse problem solvers have demonstrated state-of-the-art performance in cases where the forward operator is known (i.e. non-blind). However, the applicability of the method to blind inverse problems has yet to be…

Computer Vision and Pattern Recognition · Computer Science 2022-11-22 Hyungjin Chung , Jeongsol Kim , Sehui Kim , Jong Chul Ye

We consider a class of inverse problems characterized by forward operators that are partially specified, non-smooth, and non-differentiable. Although generative inverse solvers have made significant progress, we find that these forward…

Computer Vision and Pattern Recognition · Computer Science 2026-03-13 Sattwik Basu , Chaitanya Amballa , Zhongweiyang Xu , Jorge Vančo Sampedro , Srihari Nelakuditi , Romit Roy Choudhury

Diffusion models are commonly interpreted as learning the score function, i.e., the gradient of the log-density of noisy data. However, this assumption implies that the target of learning is a conservative vector field, which is not…

Machine Learning · Computer Science 2025-09-03 An B. Vuong , Michael T. McCann , Javier E. Santos , Yen Ting Lin

Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers,…

Computer Vision and Pattern Recognition · Computer Science 2025-10-06 Hyungjin Chung , Dohoon Ryu , Michael T. McCann , Marc L. Klasky , Jong Chul Ye

Inverse medium scattering solvers generally reconstruct a single solution without an associated measure of uncertainty. This is true both for the classical iterative solvers and for the emerging deep learning methods. But ill-posedness and…

Machine Learning · Computer Science 2022-12-12 AmirEhsan Khorashadizadeh , Ali Aghababaei , Tin Vlašić , Hieu Nguyen , Ivan Dokmanić

Bayesian full waveform inversion (FWI) offers uncertainty-aware subsurface models; however, posterior sampling directly on observed seismic shot records is rarely practical at the field scale because each sample requires numerous…

Geophysics · Physics 2025-12-16 Mohammad H. Taufik , Tariq Alkhalifah

Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse…

Flow matching is a recent state-of-the-art framework for generative modeling based on ordinary differential equations (ODEs). While closely related to diffusion models, it provides a more general perspective on generative modeling. Although…

Computer Vision and Pattern Recognition · Computer Science 2025-03-12 Jeongsol Kim , Bryan Sangwoo Kim , Jong Chul Ye

Diffusion models have emerged as powerful tools for solving inverse problems due to their exceptional ability to model complex prior distributions. However, existing methods predominantly assume known forward operators (i.e., non-blind),…

Computer Vision and Pattern Recognition · Computer Science 2024-07-02 Weimin Bai , Siyi Chen , Wenzheng Chen , He Sun

Recent studies on inverse problems have proposed posterior samplers that leverage the pre-trained diffusion models as powerful priors. These attempts have paved the way for using diffusion models in a wide range of inverse problems.…

Computer Vision and Pattern Recognition · Computer Science 2024-07-24 Sojin Lee , Dogyun Park , Inho Kong , Hyunwoo J. Kim

Diffusion models have recently been recognised as efficient inverse problem solvers due to their ability to produce high-quality reconstruction results without relying on pairwise data training. Existing diffusion-based solvers utilize…

Computer Vision and Pattern Recognition · Computer Science 2024-03-12 Linchao He , Hongyu Yan , Mengting Luo , Hongjie Wu , Kunming Luo , Wang Wang , Wenchao Du , Hu Chen , Hongyu Yang , Yi Zhang , Jiancheng Lv

Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we reveal that recent methods can be uniformly interpreted as employing a…

Computer Vision and Pattern Recognition · Computer Science 2024-06-04 Xinyu Peng , Ziyang Zheng , Wenrui Dai , Nuoqian Xiao , Chenglin Li , Junni Zou , Hongkai Xiong

Imaging inverse problems can be solved in an unsupervised manner using pre-trained diffusion models, but doing so requires approximating the gradient of the measurement-conditional score function in the diffusion reverse process. We show…

Computer Vision and Pattern Recognition · Computer Science 2025-08-28 Matt C. Bendel , Saurav K. Shastri , Rizwan Ahmad , Philip Schniter

Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several…

Machine Learning · Computer Science 2024-12-24 Henry Li , Marcus Pereira

A nonlinear diffusion equation, interpreted as a Wasserstein gradient flow, is numerically solved in one space dimension using a higher-order minimizing movement scheme based on the BDF (backward differentiation formula) discretization. In…

Numerical Analysis · Mathematics 2015-09-02 Bertram Düring , Philipp Fuchs , Ansgar Jüngel

Diffusion models and flow-based methods have shown impressive generative capability, especially for images, but their sampling is expensive because it requires many iterative updates. We introduce W-Flow, a framework for training a…

Machine Learning · Computer Science 2026-05-28 Jiaqi Han , Puheng Li , Qiushan Guo , Renyuan Xu , Stefano Ermon , Emmanuel J. Candès

Diffusion models have achieved remarkable progress in universal image restoration. While existing methods speed up inference by reducing sampling steps, substantial step intervals often introduce cumulative errors. Moreover, they struggle…

Computer Vision and Pattern Recognition · Computer Science 2025-05-09 Hebaixu Wang , Jing Zhang , Haonan Guo , Di Wang , Jiayi Ma , Bo Du

Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusion models are repurposed for solving inverse problems using…

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…

Machine Learning · Computer Science 2024-05-21 Hyungjin Chung , Byeongsu Sim , Dohoon Ryu , Jong Chul Ye

In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…

Fluid Dynamics · Physics 2025-07-14 Yannick Gachnang , Vismay Churiwala