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We develop an approach to training generative models based on unrolling a variational autoencoder into a Markov chain, and shaping the chain's trajectories using a technique inspired by recent work in Approximate Bayesian computation. We show that the global minimizer of the resulting objective is achieved when the generative model reproduces the target distribution. To allow finer control over the behavior of the models, we add a regularization term inspired by techniques used for regularizingdblp:conf/icml/BachmanP15 fatcat:pyq33sdwdncilo7k5msdn7da5a