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In this contribution, we propose a new computationally efficient method tocombine Variational Inference (VI) with Markov Chain Monte Carlo (MCMC). Thisapproach can be used with generic MCMC kernels, but is especially well suitedto \textit{MetFlow}, a novel family of MCMC algorithms we introduce, in whichproposals are obtained using Normalizing Flows. The marginal distributionproduced by such MCMC algorithms is a mixture of flow-based distributions, thusdrastically increasing the expressivity of the variational family. Unlikeprevious methods following this direction, our approach is amenable to thereparametrization trick and does not rely on computationally expensive reversekernels. Extensive numerical experiments show clear computational andperformance improvements over state-of-the-art methods.

MetFlow: A New Efficient Method for Bridging the Gap between Markov Chain Monte Carlo and Variational Inference