  We propose Continual Repeated Annealed Flow Transport Monte Carlo (CRAFT), a
method that combines a sequential Monte Carlo (SMC) sampler (itself a
generalization of Annealed Importance Sampling) with variational inference
using normalizing flows. The normalizing flows are directly trained to
transport between annealing temperatures using a KL divergence for each
transition. This optimization objective is itself estimated using the
normalizing flow/SMC approximation. We show conceptually and using multiple
empirical examples that CRAFT improves on Annealed Flow Transport Monte Carlo
(Arbel et al., 2021), on which it builds and also on Markov chain Monte Carlo
(MCMC) based Stochastic Normalizing Flows (Wu et al., 2020). By incorporating
CRAFT within particle MCMC, we show that such learnt samplers can achieve
impressively accurate results on a challenging lattice field theory example.
