SAN: Inducing Metrizability of GAN with Discriminative Normalized Linear Layer

TL;DR

This paper introduces SAN, a new GAN training method that ensures the discriminator acts as a proper distance measure, leading to improved generative performance and state-of-the-art results on ImageNet class-conditional generation.

Contribution

The paper derives conditions for the discriminator to serve as a distribution distance and proposes SAN, a simple modification applicable to many GANs for improved training stability and quality.

Findings

SAN improves GAN training stability and quality.

SAN achieves state-of-the-art FID scores on ImageNet 256x256.

Theoretical connection between GANs and sliced optimal transport.

Abstract

Generative adversarial networks (GANs) learn a target probability distribution by optimizing a generator and a discriminator with minimax objectives. This paper addresses the question of whether such optimization actually provides the generator with gradients that make its distribution close to the target distribution. We derive metrizable conditions, sufficient conditions for the discriminator to serve as the distance between the distributions by connecting the GAN formulation with the concept of sliced optimal transport. Furthermore, by leveraging these theoretical results, we propose a novel GAN training scheme, called slicing adversarial network (SAN). With only simple modifications, a broad class of existing GANs can be converted to SANs. Experiments on synthetic and image datasets support our theoretical results and the SAN's effectiveness as compared to usual GANs. Furthermore, we also apply SAN to StyleGAN-XL, which leads to state-of-the-art FID score amongst GANs for class conditional generation on ImageNet 256$\times$256. Our implementation is available on https://ytakida.github.io/san.