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
The paper introduces RED-KLwSGS, a new posterior sampling method for Bayesian imaging inverse problems that combines exact Gaussian updates for the data variable with underdamped (kinetic) Langevin diffusion for the auxiliary variable, driven by a one‑shot denoising score. It achieves the same per‑iteration cost as existing Langevin‑within‑SGS samplers while providing non‑asymptotic Wasserstein‑2 convergence guarantees for strongly log‑concave priors. A further variant, Joint-RED-KLwSGS, applies kinetic Langevin diffusion to both variables, and experiments using denoising diffusion probabilistic models on FFHQ and ImageNet demonstrate faster convergence and high‑quality image reconstruction.
By Dai Hai Nguyen, Duc Dung Nguyen
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
The paper introduces flow matching as an amortized alternative to Markov chain Monte Carlo for sampling from posterior distributions in Bayesian inverse problems. By training a transport map on joint samples of parameters and data, the method produces independent approximate posterior samples for any observation at negligible online cost, eliminating the need for new likelihood evaluations. The authors provide accuracy estimates in total‑variation distance and Kullback‑Leibler divergence, propose a hybrid Metropolized sampler for exactness, and validate the approach on examples such as electrical impedance tomography and a likelihood‑free Lotka‑Volterra model.
By Jan Blechschmidt, Oliver G. Ernst, Moritz Poguntke, Bj\"orn Sprungk
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:2606.22346v2 Announce Type: replace-cross
Abstract: Principled regression for stochastic processes is a long-standing challenge with deep connections to scientific inverse problems. We introduc...
By Yaozhong Shi, Zachary E. Ross, Yisong Yue
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
arXiv:2602. 11059v2 Announce Type: replace-cross Abstract: This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive error, (2) the problem is ill-posed and regularization relies on a Bayesian strategy, (3)~the prior is modeled by a diffusion process adjusted on an available large set of examples.
By Jean-Fran\c{c}ois Giovannelli
arXiv:2606. 26592v1 Announce Type: cross Abstract: We propose latent-space diffusion posterior sampling (L-DPS), an approximate Bayesian framework for high-dimensional inverse problems governed by partial differential equations (PDEs).
By Yuanzhe Wang, Alexandre M. Tartakovsky
arXiv:2609.37529v1 Announce Type: cross
Abstract: Pretrained denoisers provide a powerful way to incorporate image priors into restoration algorithms. Plug-and-Play and RED approaches exploit fixed-n...
By Alexandre Lagier, Valentine Tosel, Anne Gagneux, Mathurin Massias, S\'egol\`ene Martin
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
PosteriorBench is a new benchmark that evaluates how well generative inverse solvers recover full posterior distributions rather than just a single reconstruction. It tests four physics-based inverse problems—Darcy flow inversion, Poisson source recovery, carbon capture and storage, and light transport material inference—using high-fidelity reference posteriors generated by rejection sampling and MCMC. The benchmark employs five metrics (posterior-mean error, posterior-standard-deviation error, maximum mean discrepancy, sliced Wasserstein distance, and radially averaged power-spectrum error) to assess pointwise accuracy, uncertainty, distributional alignment, and global frequency fidelity, revealing significant distribution-matching gaps in current solvers and highlighting the importance of neural operators, guidance weights, and generation noise for posterior-variance calibration.
By Jiachen Yao, Zi-Siang Hsu, Xi Deng, Aditi Gupta, Xin Ju, Sally M Benson, Gege Wen, Anima Anandkumar