Optimal Transport offers an alternative to maximum likelihood for learning generative autoencoding models. We show how this principle dictates the minimization of the Wasserstein distance between the encoder aggregated posterior and the prior, plus a reconstruction error. We prove that in the non-parametric limit the autoencoder generates the data distribution if and only if the two distributions match exactly, and that the optimum can be obtained by deterministic autoencoders. We then introduce the Sinkhorn AutoEncoder (SAE), which casts the problem into Optimal Transport on the latent space. The resulting Wasserstein distance is minimized by backpropagating through the Sinkhorn algorithm. SAE models the aggregated posterior as an implicit distribution and therefore does not need a reparameterization trick for gradients estimation. Moreover, it requires virtually no adaptation to different prior distributions. We demonstrate its flexibility by considering models with hyperspherical and Dirichlet priors, as well as a simple case of probabilistic programming. SAE matches or outperforms other autoencoding models in visual quality and FID scores.

本文介绍了一种基于最优输运的生成自编码模型的学习方法，将生成器与真实数据分布的p-Wasserstein距离最小化等价于最小化编码器聚合后验概率与潜在空间先验的p-Wasserstein距离，加上重构误差。 文章还介绍了一种称为Sinkhorn自编码器（SAE）的算法，通过Sinkhorn算法进行反向传播来近似和最小化潜在空间中的p-Wasserstein距离。