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 continuous normalizing flow-based approach designed to sample from high-dimensional and multi-modal distributions. The key idea is to learn a continuous normalizing flow-based transport map, guided by annealing, to transition samples from an easy-to-sample distribution to the target distribution, facilitating effective exploration of modes in high-dimensional spaces. Unlike many existing methods, AF training does not rely on samples from the target distribution. AF ensures effective and balanced mode exploration, achieves linear complexity in sample size and dimensions, and circumvents inefficient mixing times. 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 the potential of AF for sampling the least favorable distributions.

翻译：从高维多模态分布中采样仍然是统计贝叶斯推断和基于物理的机器学习等领域面临的基础性挑战。本文提出退火流（AF），一种基于连续标准化流的方法，旨在从高维多模态分布中采样。其核心思想是学习一个由退火过程引导的、基于连续标准化流的传输映射，将样本从易于采样的分布逐步过渡到目标分布，从而促进对高维空间中模态的有效探索。与许多现有方法不同，AF的训练不依赖于来自目标分布的样本。AF确保了有效且均衡的模态探索，实现了样本规模和维度上的线性复杂度，并规避了低效的混合时间。我们通过对各种具有挑战性的分布和真实世界数据集（特别是在高维和多模态场景下）的大量实验，证明了AF相较于现有先进方法的优越性能。我们还强调了AF在采样最不利分布方面的潜力。