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This research introduces a deep unfolding framework to replace computationally expensive MCMC steps in Split-Gibbs diffusion sampling, significantly lowering costs for nonlinear inverse problems like phase retrieval. By reformulating Gibbs updates as Gaussian denoising tasks within an ODE diffusion model, the method enables parallelization and removes the need for algorithm-specific tuning while reusing pretrained priors.
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.
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.
Signal Processing (eess.SP); Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2609.30539 [eess.SP]
(or arXiv:2609.30539v1 [eess.SP] for this version)
https://doi.org/10.48550/arXiv.2609.30539 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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