Sampling from multi-modal distributions with polynomial query complexity in fixed dimension via reverse diffusion

Adrien Vacher, Omar Chehab, Anna Korba

Keywords: Diffusion, Sampling, Multi-modal, Complexity

Abstract: 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.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 13005