Scale-Consistent Posterior Dynamics for Diffusion Inverse Problems

[2608.15144] A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Machine Learning arXiv:2608.15144 (stat) [Submitted on 15 Aug 2026 ( v1 ), last revised 3 Sep 2026 (this version, v2)] Title: A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors Authors: Zhaoqiang Liu , Tongyao Pang , Ruibing Wang , Yang Zheng View a PDF of the paper titled A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors, by Zhaoqiang Liu and 3 other authors View PDF HTML (experimental) Abstract: Pretrained diffusion models represent image distributions through a continuum of progressively smoothed distributions. This multiscale structure organizes generation from global structure to fine detail and supports high-quality, diverse samples. We exploit the same multiscale diffusion prior for linear imaging inverse problems. Rather than using the pretrained model only as a denoiser in an outer iteration, we define a surrogate likelihood whose center is aligned with the clean-image coordinate and whose covariance accounts for residual diffusion uncertainty. This construction defines an explicit surrogate posterior path, from which we derive continuous posterior dynamics. A tunable Langevin component supports target tracking and allows the amount of posterior exploration to be adapted to the application. We prove endpoint consistency and a finite-horizon tracking bound and, in the exact-score setting, first-order weak accuracy. For computation, we derive the Posterior-Dynamics Implicit--Explicit sampler (PD-IMEX), a stable method using one score evaluation per diffusion scale and an implicit data-consistency update. Experiments on deblurring, super-resolution, and inpainting show strong reconstruction quality at 100 score evaluations, coarse-grid stability, and controllable fidelity--diversity behavior. Comments: 26 pages, 5 figures, 3 tables Subjects: Machine Learning (stat.ML) ; Artificial Intelligence (cs.AI); Machine Learning (cs.LG) MSC classes: 65J22, 65C30, 62C10, 68T07, 94A08 Cite as: arXiv:2608.15144 [stat.ML] (or arXiv:2608.15144v2 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2608.15144 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Tongyao Pang [ view email ] [v1] Sat, 15 Aug 2026 09:38:41 UTC (7,872 KB) [v2] Thu, 3 Sep 2026 10:21:53 UTC (2,333 KB) Full-text links: Access Paper: View a PDF of the paper titled A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors, by Zhaoqiang Liu and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: stat.ML < prev | next > new | recent | 2026-08 Change to browse by: cs cs.AI cs.LG stat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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