In Defence Of Wasserstein

Ariel Elnekave, Yair Weiss

Primary Area: generative models

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Keywords: GAN, Wasserstein, Optimal transport, Image patches, Generative models

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TL;DR: A defence of the distribution-minimization percpective of GANs. WGANS with CNN discriminator match patch distributions.

Abstract:

Since the introduction of Wasserstein GANs, there has been considerable debate whether they should be viewed as minimizing the Wasserstein distance between the training images and the generated images. In particular, several recent works have shown that minimizing this Wasserstein distance leads to blurry images that are of much lower quality than those generated by state-of-the-art WGANs.
In this paper we present theoretical and experimental results that suggest that with the appropriate parameter settings, WGANs $\textbf{do}$ minimize the Wasserstein distance but the form of the distance that is minimized depends highly on the discriminator architecture. We focus on discrete generators for which the Wasserstein distance between the generator distribution and the training distribution can be computed exactly and show that when the discriminator is fully connected, standard WGANs indeed minimize the Wasserstein distance between the generated images and the training images, while when the discriminator is convolutional they minimize the Wasserstein distance between $\textbf{patches}$ in the generated images and the training images. Our experiments indicate that minimizing the patch Wasserstein metric yields sharp and realistic samples for the same datasets in which minimizing the image Wasserstein distance yields blurry and low quality samples. Our results also suggest alternative methods that directly optimize the patch Wasserstein distance without a discriminator and/or a generator.

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Submission Number: 3136