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 methods, or use stochastic losses that have 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 apply FAB to 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, 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 the samples, we obtain unbiased histograms of dihedral angles that are almost identical to the ground truth.

翻译：归一化流是可处理的密度模型，能够近似复杂的目标分布，例如物理系统的玻尔兹曼分布。然而，当前训练流的方法要么存在模式寻求行为，要么依赖于事先通过昂贵MCMC方法生成的目标样本，要么使用方差较高的随机损失函数。为避免这些问题，我们将流与退火重要性采样相结合，并最小化覆盖质量的$\alpha=2$散度，从而最小化重要性权重方差。我们的方法——流退火重要性采样自举，利用AIS在流对目标近似较差的区域生成样本，有助于发现新模态。我们将FAB应用于多模态目标，并展示其在先前方法失效的情况下仍能非常精确地近似这些目标。据我们所知，我们是首个仅利用未归一化目标密度学习丙氨酸二肽分子玻尔兹曼分布的方法，无需通过分子动力学模拟生成样本：FAB在比基于MD样本的最大似然训练少用100倍目标评估次数的条件下取得了更优的结果。经过样本重加权后，我们获得了与真实分布几乎完全一致的二面角无偏直方图。