Even in low dimensions, sampling from multi-modal distributions is challenging. We provide the first sampling algorithm for a broad class of distributions -- including all Gaussian mixtures -- with a query complexity that is polynomial in the parameters governing multi-modality, assuming fixed dimension. Our sampling algorithm simulates a time-reversed diffusion process, using a self-normalized Monte Carlo estimator of the intermediate score functions. Unlike previous works, it avoids metastability, requires no prior knowledge of the mode locations, and relaxes the well-known log-smoothness assumption which excluded general Gaussian mixtures so far.

翻译：即使在低维度下，从多模态分布中采样仍具有挑战性。我们针对一类广泛的分布——包括所有高斯混合分布——提出了首个采样算法，其查询复杂度在控制多模态性的参数上呈多项式级，且假设维度固定。该采样算法通过模拟时间反向扩散过程实现，使用中间得分函数的自归一化蒙特卡洛估计器。与先前工作不同，本方法避免了亚稳态问题，无需预先获知模态位置，并放宽了长期以来将一般高斯混合分布排除在外的经典对数平滑性假设。