Sampling from high dimensional, multimodal distributions remains a fundamental challenge across domains such as statistical Bayesian inference and physics based machine learning. In this paper, we propose Annealing Flow, a continuous normalizing flow based approach designed to sample from high dimensional and multimodal 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 multimodal settings. We also highlight the potential of AF for sampling the least favorable distributions.

翻译：从高维、多模态分布中采样是统计贝叶斯推断和基于物理的机器学习等领域面临的一项基础性挑战。本文提出退火流，一种基于连续归一化流的方法，旨在从高维、多模态分布中采样。其核心思想是学习一个基于连续归一化流的传输映射，该映射在退火过程的引导下，将样本从易于采样的分布逐步转移至目标分布，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，退火流的训练不依赖于来自目标分布的样本。该方法确保了有效且均衡的模态探索，实现了样本量与维度的线性复杂度，并规避了低效的混合时间。通过在多种具有挑战性的分布和真实世界数据集（尤其是高维与多模态场景）上进行大量实验，我们证明了退火流相较于现有先进方法的优越性能。我们还强调了退火流在采样最不利分布方面的潜力。