Bridging the Gap Between $f$-GANs and Wasserstein GANs

TL;DR

This paper introduces KL-WGAN, a new GAN variant that unifies $f$-GANs and Wasserstein GANs, leading to improved empirical performance and state-of-the-art results on image generation tasks.

Contribution

It proposes a novel objective that bridges $f$-GANs and WGANs, enhancing theoretical understanding and practical effectiveness.

Findings

KL-WGAN achieves state-of-the-art FID scores on CIFAR10.

Empirical success on synthetic datasets and real-world images.

Unifies critic objectives of $f$-GANs and WGANs.

Abstract

Generative adversarial networks (GANs) have enjoyed much success in learning high-dimensional distributions. Learning objectives approximately minimize an $f$-divergence ($f$-GANs) or an integral probability metric (Wasserstein GANs) between the model and the data distribution using a discriminator. Wasserstein GANs enjoy superior empirical performance, but in $f$-GANs the discriminator can be interpreted as a density ratio estimator which is necessary in some GAN applications. In this paper, we bridge the gap between $f$-GANs and Wasserstein GANs (WGANs). First, we list two constraints over variational $f$-divergence estimation objectives that preserves the optimal solution. Next, we minimize over a Lagrangian relaxation of the constrained objective, and show that it generalizes critic objectives of both $f$-GAN and WGAN. Based on this generalization, we propose a novel practical objective, named KL-Wasserstein GAN (KL-WGAN). We demonstrate empirical success of KL-WGAN on synthetic datasets and real-world image generation benchmarks, and achieve state-of-the-art FID scores on CIFAR10 image generation.