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This short article revisits some of the ideas introduced in arXiv:1701.07875and arXiv:1705.07642 in a simple setup. This sheds some lights on theconnexions between Variational Autoencoders (VAE), Generative AdversarialNetworks (GAN) and Minimum Kantorovitch Estimators (MKE).

GAN and VAE from an Optimal Transport Point of View