arXiv：cs.LG· Dai Hai Nguyen, Duc Dung Nguyen·· 4 小时前AI 评分33
RED-KLwSGS：用 Kinetic Langevin 加速扩散先验下的后验采样
Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
AI 导读
研究者提出 RED-KLwSGS，在 Split Gibbs 采样（SGS）框架中保留数据变量的精确高斯更新，改用欠阻尼（kinetic）Langevin 扩散配合单次去噪得分更新辅助变量，单次迭代开销与 Langevin-within-SGS 持平，并在强对数凹先验下证明了连续与离散时间的非渐近 Wasserstein-2 收敛。
正文
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.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.10187 [stat.ML] |
| (or arXiv:2610.10187v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10187 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Dai Hai Nguyen [view email]
[v1]
Wed, 7 Oct 2026 14:53:32 UTC (26,423 KB)
来源：arXiv：cs.LG · arxiv.org