发表机构
Hokkaido University; Institute of Information Technology, VAST（北海道大学; 越南科学技术翰林院信息技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出RED-KLwSGS及其联合变体，将动力学朗之万扩散与分裂吉布斯采样结合，以加速成像逆问题的后验采样，并证明非渐近收敛性，实验显示更快收敛和高质量重建。
AI 中文摘要
分裂吉布斯采样（SGS）是贝叶斯成像逆问题中后验采样的流行框架。它通过辅助变量将高斯数据保真项与复杂先验解耦，从而数据变量被精确更新，仅先验侧的条件分布难以采样。现有采样器以两种方式之一处理该条件分布。即插即用SGS在每次迭代中运行多步扩散去噪器，这既昂贵又缺乏非渐近保证。SGS内朗之万方法采用廉价的过阻尼朗之万步骤，但需要多次迭代。我们提出RED-KLwSGS，该方法保留数据变量的精确高斯更新，并通过一次性去噪分数驱动的欠阻尼（动力学）朗之万扩散更新辅助变量，其每次迭代成本与SGS内朗之万方法相同。我们证明了在强对数凹先验下，连续和离散时间中的非渐近Wasserstein-2收敛性。我们还引入了Joint-RED-KLwSGS，将动力学朗之万扩散应用于两个变量。使用去噪扩散概率模型作为扩散先验在FFHQ和ImageNet数据集上的实验表明，该方法收敛更快且图像重建质量高。
英文摘要
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.
