The inadequate mixing of conventional Markov Chain Monte Carlo (MCMC) methods for multi-modal distributions presents a significant challenge in practical applications such as Bayesian inference and molecular dynamics. Addressing this, we propose Diffusive Gibbs Sampling (DiGS), an innovative family of sampling methods designed for effective sampling from distributions characterized by distant and disconnected modes. DiGS integrates recent developments in diffusion models, leveraging Gaussian convolution to create an auxiliary noisy distribution that bridges isolated modes in the original space and applying Gibbs sampling to alternately draw samples from both spaces. A novel Metropolis-within-Gibbs scheme is proposed to enhance mixing in the denoising sampling step. DiGS exhibits a better mixing property for sampling multi-modal distributions than state-of-the-art methods such as parallel tempering, attaining substantially improved performance across various tasks, including mixtures of Gaussians, Bayesian neural networks and molecular dynamics.

翻译：传统马尔可夫链蒙特卡洛（MCMC）方法在处理多峰分布时混合不充分，这在贝叶斯推断和分子动力学等实际应用中构成了重大挑战。针对此问题，我们提出了扩散吉布斯采样（DiGS），这是一类创新的采样方法，旨在有效采样具有相距遥远且互不连通的众数的分布。DiGS融合了扩散模型的最新进展，利用高斯卷积创建一个辅助的噪声分布，该分布能桥接原始空间中孤立的众数，并应用吉布斯采样交替地从两个空间中抽取样本。我们提出了一种新颖的“吉布斯框架内的Metropolis”方案，以增强去噪采样步骤中的混合效果。在采样多峰分布时，DiGS展现出比并行回火等先进方法更优的混合特性，在高斯混合模型、贝叶斯神经网络和分子动力学等多种任务中均取得了显著提升的性能。