FlowSGS introduces a flow-based posterior sampling method that combines Split Gibbs Sampling with annealed coupling and Stochastic Interpolants to improve flow priors for inverse imaging. The approach includes a novel timestep correction and accelerated warm-up using one-step flow models, resulting in faster and more accurate performance across various imaging tasks. It also demonstrates the first application of flow-based samplers to a nonlinear inverse problem, namely Fourier phase retrieval, and extends one-step flow models to principled Bayesian inverse imaging.
By Tianao Li, Xinhui Qian, Emma Alexander
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 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
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
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: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: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: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 Retrieval-Augmented Initialization with Dual-Guided Inversion (RA‑DGI), a method that improves the initial noise used by flow‑based inverse problem solvers by leveraging retrieved proxy clean images and dual‑guided inversion. Experiments across multiple inverse problems show that this improved initialization significantly enhances reconstruction fidelity and perceptual performance compared to standard random noise and inference‑time scaling strategies, while adding less computational overhead.
By Hansam Cho, Seoung Bum Kim
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
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
The paper introduces FLINT, a two‑stage framework for flow‑matching inverse problems that couples proximal initialization with bounded stochasticity. It shows that a moderately optimized proximal source initialization can reach a performance plateau, but this advantage is lost if stochasticity accumulates too much during guided sampling. FLINT first establishes a high‑fidelity starting point via a manifold‑constrained proximal objective, then performs guided sampling under a bounded stochasticity schedule, achieving state‑of‑the‑art perceptual quality and competitive distortion metrics with superior computational efficiency.
By Junseo Bang, Daewon Choi, Dong Ju Mun, Se Young Chun