Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors

2026-10-07

AI Summary

This study addresses the high computational cost and slow convergence of sampling for Bayesian imaging inverse problems under diffusion priors by proposing the RED-KLwSGS algorithm. This method introduces underdamped kinetic Langevin dynamics into the Split Gibbs framework for the first time, enabling efficient auxiliary variable updates via a single denoising score to achieve rapid posterior sampling. Theoretically, non-asymptotic Wasserstein-2 convergence guarantees are established under strongly log-concave priors. Experimentally, evaluations on the FFHQ and ImageNet datasets demonstrate that the proposed approach significantly accelerates convergence compared to baseline methods while generating high-quality reconstructed images.

Abstract

Split Gibbs sampling (SGS) is a popular framework for posterior sampling in Bayesian imaging inverse problems. It decouples a Gaussian data-fidelity term from a complex prior through an auxiliary variable, so the data variable is updated exactly and only the prior-side conditional is hard to sample. Existing samplers treat this conditional in one of two ways. Plug-and-play SGS runs a multi-step diffusion denoiser at every iteration, which is expensive and lacks non-asymptotic guarantees. Langevin-within-SGS takes cheap overdamped Langevin steps but needs many iterations. We propose RED-KLwSGS, which keeps the exact Gaussian update for the data variable and updates the auxiliary variable with underdamped (kinetic) Langevin diffusions driven by a one-shot denoising score, at the same per-iteration cost as Langevin-within-SGS. We prove non-asymptotic Wasserstein-2 convergence in continuous and discrete time for strongly log-concave priors. We also introduce Joint-RED-KLwSGS, which applies kinetic Langevin diffusions to both variables. Experiments with Denoising diffusion probabilistic models as diffusion priors on FFHQ and ImageNet datasets show faster convergence and high-quality image reconstruction.

Problem

• Bayesian imaging inverse problems
• Split Gibbs sampling
• posterior sampling
• diffusion priors
• kinetic Langevin

Innovation

• Split Gibbs Sampling
• Kinetic Langevin Diffusion
• Diffusion Priors
• Posterior Sampling
• Inverse Problems