  In this contribution, we propose a new computationally efficient method to
combine Variational Inference (VI) with Markov Chain Monte Carlo (MCMC). This
approach can be used with generic MCMC kernels, but is especially well suited
to \textit{MetFlow}, a novel family of MCMC algorithms we introduce, in which
proposals are obtained using Normalizing Flows. The marginal distribution
produced by such MCMC algorithms is a mixture of flow-based distributions, thus
drastically increasing the expressivity of the variational family. Unlike
previous methods following this direction, our approach is amenable to the
reparametrization trick and does not rely on computationally expensive reverse
kernels. Extensive numerical experiments show clear computational and
performance improvements over state-of-the-art methods.
