Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding

arXiv:2609.30539v1 Announce Type: cross 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

• A Gibbs posterior sampler for inverse problem based on prior diffusion model
• Estimation of instrument and noise parameters for inverse problem based on prior diffusion model
• Provable Diffusion Posterior Sampling for Bayesian Inversion
• PSI3D: Plug-and-Play 3D Stochastic Inference with Slice-wise Latent Diffusion Prior
• Sparse Scheduled Diffusion Guidance for Inverse Problems

Source: arXiv cs.LG | 2026-09-28