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. Our approach exhibits a better mixing property for sampling multi-modal distributions than state-of-the-art methods such as parallel tempering. We demonstrate that our sampler attains substantially improved results 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。针对这一问题，我们提出了扩散吉布斯采样（DiGS）——一种创新的采样方法族，专为有效采样具有远距离且不连通模态的分布而设计。DiGS融合了扩散模型的最新进展，利用高斯卷积构建一个辅助噪声分布，该分布可桥接原始空间中的孤立模态，并通过吉布斯采样交替从两个空间中抽取样本。与并行退火等最先进方法相比，我们的方法在多模态分布采样中展现出更优的混合特性。实验表明，我们的采样器在高斯混合模型、贝叶斯神经网络和分子动力学等多项任务中均取得了显著改进的结果。