A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
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.
Related
- Accelerating posterior sampling in Bayesian inverse problems with diffusion models: an online-offline perspective
- Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
- A Shifted Balanced Polynomial Collocation Framework for Variable-Coefficient Multi-Term Time-Fractional Convection–Diffusion–Reaction Problems
- Posterior Consistency under dependent errors in non-linear inverse problems with applications to time evolution equations
- Flow Annealing Posterior Sampling for Function-Space Regression and Inverse Problems
BibTeX
@misc{liu2026posteriordynamics,
title = {{A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors}},
author = {Zhaoqiang Liu and Tongyao Pang and Ruibing Wang and Yang Zheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.15144},
eprint = {2608.15144},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.15144},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
AU - Zhaoqiang Liu
AU - Tongyao Pang
AU - Ruibing Wang
AU - Yang Zheng
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2608.15144
UR - https://arxiv.org/abs/2608.15144
AB - 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.
ER -