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In this paper we study generative modeling via autoencoders while using theelegant geometric properties of the optimal transport (OT) problem and theWasserstein distances. We introduce Sliced-Wasserstein Autoencoders (SWAE),which are generative models that enable one to shape the distribution of thelatent space into any samplable probability distribution without the need fortraining an adversarial network or defining a closed-form for the distribution.In short, we regularize the autoencoder loss with the sliced-Wassersteindistance between the distribution of the encoded training samples and apredefined samplable distribution. We show that the proposed formulation has anefficient numerical solution that provides similar capabilities to WassersteinAutoencoders (WAE) and Variational Autoencoders (VAE), while benefiting from anembarrassingly simple implementation.

Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model