  Many problems in the physical sciences, machine learning, and statistical
inference necessitate sampling from a high-dimensional, multi-modal probability
distribution. Markov Chain Monte Carlo (MCMC) algorithms, the ubiquitous tool
for this task, typically rely on random local updates to propagate
configurations of a given system in a way that ensures that generated
configurations will be distributed according to a target probability
distribution asymptotically. In high-dimensional settings with multiple
relevant metastable basins, local approaches require either immense
computational effort or intricately designed importance sampling strategies to
capture information about, for example, the relative populations of such
basins. Here we analyze an adaptive MCMC which augments MCMC sampling with
nonlocal transition kernels parameterized with generative models known as
normalizing flows. We focus on a setting where there is no preexisting data, as
is commonly the case for problems in which MCMC is used. Our method uses: (i) a
MCMC strategy that blends local moves obtained from any standard transition
kernel with those from a generative model to accelerate the sampling and (ii)
the data generated this way to adapt the generative model and improve its
efficacy in the MCMC algorithm. We provide a theoretical analysis of the
convergence properties of this algorithm, and investigate numerically its
efficiency, in particular in terms of its propensity to equilibrate fast
between metastable modes whose rough location is known \textit{a~priori} but
respective probability weight is not. We show that our algorithm can sample
effectively across large free energy barriers, providing dramatic accelerations
relative to traditional MCMC algorithms.
