Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model

Scalable generative models that capture the rich and often nonlinear distribution of highdimensional data, (i.e., image, video, and audio), play a central role in various applications of machine learning, including transfer learning [14, 25], super-resolution [16, 21], image inpainting and completion [35], and image retrieval [7], among many others. The recent generative models, including Generative Adversarial Networks (GANs) [1, 2, 11, 30] and Variational Autoencoders (VAE) [5, 15, 24] enable an unsupervised and end-to-end modeling of the high-dimensional distribution of the training data. Learning such generative models boils down to minimizing a dissimilarity measure between the data distribution and the output distribution of the generative model. To this end, and following the work of Arjovsky et al. [1] and Bousquet et al. [5] we approach the problem of generative modeling from the optimal transport point of view. The optimal transport problem [18, 34] provides a way to measure the distances between probability distributions by transporting (i.e., morphing) one distribution into another.