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）方法在多模态分布中混合不充分的问题，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。为此，我们提出了扩散吉布斯采样（DiGS），这是一类创新的采样方法，旨在从具有远距离且不连通模态的分布中进行高效采样。DiGS整合了扩散模型的最新进展，利用高斯卷积构建辅助噪声分布以连接原始空间中的孤立模态，并通过吉布斯采样在两个空间之间交替抽取样本。我们提出了一种新颖的"Metropolis-within-Gibbs"方案，以增强去噪采样步骤中的混合能力。与平行回火等现有最优方法相比，DiGS在采样多模态分布时展现出更优的混合特性，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表现。