The paper introduces LUD-DIF, a diffusion-based method that solves inverse problems using unpaired data. By deriving the evidence lower bound of the joint distribution and decoupling it into two independent diffusion processes under a weak‑coupling assumption, the authors provide a variational inference framework, a loss function, and an error‑bound analysis. Experiments show that LUD‑DIF performs well across multiple image inverse problems, demonstrating its effectiveness and generalization in unpaired settings.
By Chenglong Bao, Yiming Dang, Chenguang Duan, Yuling Jiao, Defeng Sun
arXiv:2607. 19333v1 Announce Type: cross Abstract: Diffusion-based methods have achieved remarkable empirical success in solving inverse problems.
By Yuchen Jiao, Na Li, Changxiao Cai, Yuxin Chen, Gen Li
arXiv:2601. 22443v2 Announce Type: replace Abstract: Can a diffusion model trained on bedrooms recover human faces?
By Jing Jia, Wei Yuan, Sifan Liu, Liyue Shen, Guanyang Wang
arXiv:2509.19276v2 Announce Type: replace-cross
Abstract: Solving ill-posed inverse problems requires powerful and flexible priors. We propose leveraging pretrained latent diffusion models for this t...
By Tim Y. J. Wang, O. Deniz Akyildiz
arXiv:2602. 11711v2 Announce Type: replace-cross Abstract: This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems.
By Jean-Fran\c{c}ois Giovannelli
arXiv:2606. 02331v1 Announce Type: cross Abstract: Diffusion-based inverse problem solvers can produce realistic reconstructions, but realism alone does not ensure that the recovered details are supported by the measurement.
By Pengfei Jin, Yiqi Tian, Kailong Fan, Bingjie Qi, Quanzheng Li
arXiv:2510. 02208v3 Announce Type: replace-cross Abstract: Diffusion models have emerged as powerful generative priors for solving inverse imaging problems.
By Amirreza Tanevardi, Pooria Abbas Rad Moghadam, Seyed Mohammad Eshtehardian, Sajjad Amini, Babak Khalaj
The paper introduces a Posterior‑Dynamics Framework that leverages pretrained diffusion models as multiscale priors for linear imaging inverse problems such as deblurring, super‑resolution, and inpainting. By constructing a surrogate likelihood centered on the clean image and incorporating diffusion uncertainty, the authors derive continuous posterior dynamics and a tunable Langevin component for adaptive exploration. They prove theoretical guarantees (endpoint consistency, finite‑horizon tracking, weak accuracy) and present the PD‑IMEX sampler, which achieves high‑quality reconstructions with only 100 score evaluations and controllable fidelity‑diversity trade‑offs.
By Zhaoqiang Liu, Tongyao Pang, Ruibing Wang, Yang Zheng
The paper introduces a perceptually regularized diffusion framework for image super‑resolution, adding perceptual‑loss based regularization to the standard diffusion training objective. This approach incorporates prior knowledge to improve training convergence and encourages the recovery of meaningful image features. Experiments on benchmark datasets show enhanced perceptual quality while maintaining competitive distortion metrics.
By Chuxiangbo Wang, Pavithra Venkatachalapathy, Ying Liang, Min Wang, Jing Qin, Yifei Lou, Weihong Guo
The paper introduces an active diffusion-based inverse problem solver that trains a diffusion model to map between parameter and observable spaces. By iteratively detecting and correcting model misspecification through posterior uncertainty, the method can discover and learn the correct parameter region even when initial training bounds exclude the true parameters. The authors demonstrate the solver on a toy inverse problem with infinite solutions and on parameterizing quantum correlation functions for a Quantum Chromodynamics analysis of nucleon structure.
By Jitao Xu, Nobuo Sato, Yaohang Li
arXiv:2606. 17048v1 Announce Type: new Abstract: Diffusion and flow-based models learn powerful data priors by training a denoiser to reverse Gaussian corruption.
By Abbas Mammadov, Ozgur Kara, Kaan Oktay, Iskander Azangulov, Adil Kaan Akan, Hyungjin Chung, James Matthew Rehg, Yee Whye Teh
arXiv:2511. 17038v4 Announce Type: replace Abstract: From a Bayesian perspective, score-based diffusion solves inverse problems through joint inference, embedding the likelihood with the prior to guide the sampling process.
By Hao Chen, Renzheng Zhang, Scott S. Howard