Sampling from multi-modal distributions with polynomial query complexity in fixed dimension via reverse diffusion
Computation
2025-10-24 v3 Machine Learning
Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.2501.00565,
title = {Sampling from multi-modal distributions with polynomial query complexity in fixed dimension via reverse diffusion},
author = {Adrien Vacher and Omar Chehab and Anna Korba},
journal= {arXiv preprint arXiv:2501.00565},
year = {2025}
}