Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
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.
Related
- Accelerating posterior sampling in Bayesian inverse problems with diffusion models: an online-offline perspective
- SULA: Robust Langevin Sampling via Drift-Diffusion Saturation
- Flow Annealing Posterior Sampling for Function-Space Regression and Inverse Problems
- Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding
- Flow Matching for Fast Posterior Sampling in Bayesian Inverse Problems
BibTeX
@misc{nguyen2026kinetic,
title = {{Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors}},
author = {Dai Hai Nguyen and Duc Dung Nguyen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10187},
eprint = {2610.10187},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10187},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
AU - Dai Hai Nguyen
AU - Duc Dung Nguyen
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10187
UR - https://arxiv.org/abs/2610.10187
AB - 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.
ER -