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.

本研究解决了从高维多模态分布中采样的挑战，提出了退火流（AF）模型，这是一种基于连续标准化流的方法。AF通过一个连续标准化流传输图学习，能够有效探索高维空间中的模式，确保在样本大小和维度上的线性复杂度，展示了其在各种复杂分布和现实数据集上的强大性能。

退火流生成模型用于高维多模态分布的采样