  We propose a new generative model, Cramer-Wold Autoencoder (CWAE). Following
WAE, we directly encourage normality of the latent space. Our paper uses also
the recent idea from Sliced WAE (SWAE) model, which uses one-dimensional
projections as a method of verifying closeness of two distributions. The
crucial new ingredient is the introduction of a new (Cramer-Wold) metric in the
space of densities, which replaces the Wasserstein metric used in SWAE. We show
that the Cramer-Wold metric between Gaussian mixtures is given by a simple
analytic formula, which results in the removal of sampling necessary to
estimate the cost function in WAE and SWAE models. As a consequence, while
drastically simplifying the optimization procedure, CWAE produces samples of a
matching perceptual quality to other SOTA models.
