Annealing Flow Generative Models Towards Sampling High-Dimensional and Multi-Modal Distributions

Abstract

Sampling from high-dimensional, multi-modal distributions remains a fundamental challenge across domains such as statistical Bayesian inference and physics-based machine learning. In this paper, we propose Annealing Flow (AF), a method built on Continuous Normalizing Flows (CNFs) for sampling from high-dimensional and multi-modal distributions. AF is trained with a dynamic Optimal Transport (OT) objective incorporating Wasserstein regularization, and guided by annealing procedures, facilitating effective exploration of modes in high-dimensional spaces. Compared to recent NF methods, AF significantly improves training efficiency and stability, with minimal reliance on MC assistance. We demonstrate the superior performance of AF compared to state-of-the-art methods through extensive experiments on various challenging distributions and real-world datasets, particularly in high-dimensional and multi-modal settings. We also highlight AF’s potential for sampling the least favorable distributions.