Annealing Flow Generative Model Towards Sampling High-Dimensional and Multi-Modal Distributions
Keywords: Continuous Normalizing Flow, Generative Model, Optimal Transport, High-Dimensional Sampling, Multi-Modal Sampling
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 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 AF’s potential for sampling the least favorable distributions.
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Submission Number: 8405
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