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