This paper introduces a stochastic plug-and-play (PnP) sampling algorithm
that leverages variable splitting to efficiently sample from a posterior
distribution. The algorithm based on split Gibbs sampling (SGS) draws
inspiration from the alternating direction method of multipliers (ADMM). It
divides the challenging task of posterior sampling into two simpler sampling
problems. The first problem depends on the likelihood function, while the
second is interpreted as a Bayesian denoising problem that can be readily
carried out by a deep generative model. Specifically, for an illustrative
purpose, the proposed method is implemented in this paper using
state-of-the-art diffusion-based generative models. Akin to its deterministic
PnP-based counterparts, the proposed method exhibits the great advantage of not
requiring an explicit choice of the prior distribution, which is rather encoded
into a pre-trained generative model. However, unlike optimization methods
(e.g., PnP-ADMM) which generally provide only point estimates, the proposed
approach allows conventional Bayesian estimators to be accompanied by
confidence intervals at a reasonable additional computational cost. Experiments
on commonly studied image processing problems illustrate the efficiency of the
proposed sampling strategy. Its performance is compared to recent
state-of-the-art optimization and sampling methods.

该论文介绍了一种基于变量拆分的随机插入算法，它使用深度生成模型解决了贝叶斯去噪问题， 与传统的优化方法相比，该方法可以提供置信区间估计。