Normalizing flows are tractable density models that can approximate complicated target distributions, e.g. Boltzmann distributions of physical systems. However, current methods for training flows either suffer from mode-seeking behavior, use samples from the target generated beforehand by expensive MCMC simulations, or use stochastic losses that have very high variance. To avoid these problems, we augment flows with annealed importance sampling (AIS) and minimize the mass covering $\alpha$-divergence with $\alpha=2$, which minimizes importance weight variance. Our method, Flow AIS Bootstrap (FAB), uses AIS to generate samples in regions where the flow is a poor approximation of the target, facilitating the discovery of new modes. We target with AIS the minimum variance distribution for the estimation of the $\alpha$-divergence via importance sampling. We also use a prioritized buffer to store and reuse AIS samples. These two features significantly improve FAB's performance. We apply FAB to complex multimodal targets and show that we can approximate them very accurately where previous methods fail. To the best of our knowledge, we are the first to learn the Boltzmann distribution of the alanine dipeptide molecule using only the unnormalized target density and without access to samples generated via Molecular Dynamics (MD) simulations: FAB produces better results than training via maximum likelihood on MD samples while using 100 times fewer target evaluations. After reweighting samples with importance weights, we obtain unbiased histograms of dihedral angles that are almost identical to the ground truth ones.

该研究提出Flow AIS Bootstrap (FAB)方法，采用退火重要性采样(AIS)和最小化质量覆盖α散度，使用的α=2，从而避免了当前训练流方法的主要问题。使用FAB将多模态目标应用于学习甘氨二肽分子的玻尔兹曼分布，证明了该方法比使用MD样本通过最大似然训练效果更好，在使用100倍少的目标评估下，可以获得与真实数据几乎相同的无偏直方图。

流退火重要性采样自助法