Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding
Abstract
Split Gibbs sampling enables diffusion posterior inference for general nonlinear inverse problems by decoupling prior and likelihood computations, allowing a pretrained diffusion prior to be reused across measurement models. However, its likelihood update often relies on iterative MCMC, which can hinder parallelization, require algorithm-specific tuning, and incur substantial computational cost. In this work, we propose a learning-based framework to replace this MCMC step by reformulating both Gibbs updates as Gaussian denoising problems and implementing them through ODE diffusion. The prior step reuses a pretrained denoiser, while the likelihood denoiser exploits known likelihood structure through a lightweight deep-unfolded network. Experiments on nonlinear phase retrieval demonstrate the effectiveness of the proposed method as an alternative to MCMC-based split Gibbs at lower likelihood-update cost.
Related
- Accelerating posterior sampling in Bayesian inverse problems with diffusion models: an online-offline perspective
- Mixed Poisson diffusion models and application to posterior sampling
- Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
- UAV SAR Imaging via Diffusion Posterior Sampling under Non-Ideal Motion in ISAC Systems
- Minimax-Optimality of Posterior Sampling for Reinforcement Learning
BibTeX
@misc{zhang2026learning,
title = {{Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding}},
author = {Yi Zhang and Rui Guo and Mengchu Xu and Zhaofeng Liu and Yonina C. Eldar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30539},
eprint = {2609.30539},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30539},
}
RIS
TY - UNPB
TI - Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding
AU - Yi Zhang
AU - Rui Guo
AU - Mengchu Xu
AU - Zhaofeng Liu
AU - Yonina C. Eldar
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30539
UR - https://arxiv.org/abs/2609.30539
AB - Split Gibbs sampling enables diffusion posterior inference for general nonlinear inverse problems by decoupling prior and likelihood computations, allowing a pretrained diffusion prior to be reused across measurement models. However, its likelihood update often relies on iterative MCMC, which can hinder parallelization, require algorithm-specific tuning, and incur substantial computational cost. In this work, we propose a learning-based framework to replace this MCMC step by reformulating both Gibbs updates as Gaussian denoising problems and implementing them through ODE diffusion. The prior step reuses a pretrained denoiser, while the likelihood denoiser exploits known likelihood structure through a lightweight deep-unfolded network. Experiments on nonlinear phase retrieval demonstrate the effectiveness of the proposed method as an alternative to MCMC-based split Gibbs at lower likelihood-update cost.
ER -