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The Generative Adversarial Networks (GAN) framework is a well-establishedparadigm for probability matching and realistic sample generation. While recentattention has been devoted to studying the theoretical properties of suchmodels, a full theoretical understanding of the main building blocks is stillmissing. Focusing on generative models with Optimal Transport metrics asdiscriminators, in this work we study how the interplay between the latentdistribution and the complexity of the pushforward map (generator) affectsperformance, from both statistical and modelling perspectives. Motivated by ouranalysis, we advocate learning the latent distribution as well as thepushforward map within the GAN paradigm. We prove that this can lead tosignificant advantages in terms of sample complexity.

Generalization Properties of Optimal Transport GANs with Latent Distribution Learning