Learning to speed up diffusion posterior sampling without MCMC
Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding
Machine Learning
Summary
Many computer vision and imaging problems require guessing the original scene from incomplete or noisy data, which often needs complex calculations. The authors study a method that helps make these guesses by breaking down the problem into easier parts, but one step was slow and hard to run in parallel because it used a random sampling method (MCMC). They replaced this slow step with a learned neural network approach that treats the problem like cleaning up noisy images, making the process faster and easier to run on modern hardware. Tests showed this new approach works well on a type of problem called nonlinear phase retrieval.
What this means in practice
- •For computational imaging engineers: Improve image reconstruction speed in nonlinear inverse problems by replacing costly sampling steps with learned denoising methods.
- •For medical imaging developers: Accelerate iterative inference algorithms in imaging modalities such as MRI by using pretrained diffusion denoisers instead of slow MCMC updates.
Authors
Yi Zhang, Rui Guo, Mengchu Xu, Zhaofeng Liu, Yonina C. Eldar
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.