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
FlowSGS introduces a flow-based posterior sampling method that combines Split Gibbs Sampling (SGS) with Langevin dynamics for the likelihood step and Stochastic Interpolants (SI) for the prior step. By integrating a pretrained flow model into the prior step via SI's reverse-time SDE and a novel timestep correction, FlowSGS reduces the number of network evaluations compared to plug‑and‑play diffusion samplers. Experiments demonstrate state‑of‑the‑art performance on various inverse problems, including the first flow‑based solution to a nonlinear inverse problem (Fourier phase retrieval).
By Tianao Li, Xinhui Qian, Emma Alexander
arXiv:2608. 15144v1 Announce Type: cross Abstract: Posterior sampling with a pretrained diffusion prior is governed by a conditional score whose intermediate likelihood component is generally intractable.
By Zhaoqiang Liu, Tongyao Pang, Ruibing Wang, Yang Zheng
The paper introduces PiX-MC, a time‑parallel posterior sampling framework that combines proximal Langevin dynamics with Picard iteration for Bayesian imaging inverse problems. By leveraging efficient proximal operators for many imaging likelihoods and exploiting parallelism across discretization nodes, PiX-MC supports multi‑GPU implementation and includes multi‑block and annealed variants to enhance scalability. Experiments on various imaging tasks, including a large‑scale sparse‑view CT problem, show that PiX‑MC can reduce runtime by up to 50× while maintaining reconstruction quality.
By Deliang Wei, Evan Bell, Wenhan Guo, Yifan Chen, Yu Sun
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
arXiv:2512. 08022v2 Announce Type: replace-cross Abstract: We propose a novel diffusion-based posterior sampling method within a plug-and-play framework.
By Jinyuan Chang, Chenguang Duan, Yuling Jiao, Ruoxuan Li, Jerry Zhijian Yang, Cheng Yuan
The paper introduces Diffusion Waltz, an MCMC algorithm that uses SDEdit-style noising and denoising as a proposal and corrects it with Metropolis-Hastings to achieve exact posterior sampling without evaluating the prior. It also incorporates observations into the proposal via a gradient‑free ensemble Kalman update while maintaining exactness. In experiments on a non‑differentiable Navier‑Stokes initial‑condition recovery problem, Diffusion Waltz outperforms existing baselines across various noise and nonlinearity regimes.
By So Takao, Gregory David Bellchambers, Luke Ye, Sanmitra Ghosh, Michalis Michaelides
The paper introduces a learning-based approach to replace the MCMC step in split-Gibbs diffusion posterior sampling. By reformulating both Gibbs updates as Gaussian denoising problems, the method uses ODE diffusion for the prior step with a pretrained denoiser and a lightweight deep-unfolded network for the likelihood step. Experiments on nonlinear phase retrieval show that this alternative reduces likelihood-update cost while maintaining effectiveness compared to MCMC-based split Gibbs.
By Yi Zhang, Rui Guo, Mengchu Xu, Zhaofeng Liu, Yonina C. Eldar
arXiv:2609.14596v1 Announce Type: new
Abstract: Training-free diffusion inverse solvers typically choose between local measurement guidance and costly clean-space posterior updates. Independent poste...
By Qi Yu, Hanlin Wu, Xiaohui Sun
Score‑based diffusion models excel at inverse problems but suffer from slow inference and task‑specific hyperparameter tuning. This paper introduces principled reparameterizations that create invariances, enabling the reuse of the same hyperparameters across different tasks. Building on the RED‑diff framework, the authors present OptDiff, a streamlined pipeline that integrates convex optimization to accelerate inference, achieving notable speedups and higher image quality in reconstruction, deblurring, and super‑resolution experiments.
By Julio Oscanoa, Irmak Sivgin, Cagan Alkan, Daniel Ennis, John Pauly, Mert Pilanci, Shreyas Vasanawala
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
The paper introduces Consecutive Posterior Fusion Denoising Diffusion Null‑Space Models (CPF‑DDNM), an inference‑time method that fuses successive measurement‑aware estimates to better recover unobservable image structures in severely ill‑posed imaging inverse problems. CPF‑DDNM builds on DDNM’s range/null‑space decomposition, preserving measurement‑determined components while refining prior‑driven null‑space estimates. Experiments on sparse‑view CT, low‑dose CT, and medical image super‑resolution demonstrate consistent improvements over DDNM and competitive performance against other diffusion‑based inverse solvers.
By Elena Morotti, Davide Evangelista, Elena Loli Piccolomini