Bridging the Gap Between f-GANs and Wasserstein GANs

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.