Bootstrap Your Flow

Normalising flows are flexible, parameterized distributions that can be used to approximate expectations from intractable distributions via importance sampling. However, current flow-based approaches are limited on challenging targets where they either suffer from mode seeking behaviour or high variance in the training loss, or rely on samples from the target distribution, which may not be available. To address these challenges, we combine flows with annealed importance sampling (AIS), while using the $\alpha$-divergence as our objective, in a novel training procedure, FAB (Flow AIS Bootstrap). Thereby, the flow and AIS to improve each other in a bootstrapping manner. We demonstrate that FAB can be used to produce accurate approximations to complex target distributions, including Boltzmann distributions, in problems where previous flow-based methods fail.