Training Wasserstein GANs without Gradient Penalties via Duality
Abstract: We propose a new method for training Wasserstein generative adversarial networks (WGANs) without using gradient penalties. We develop a novel approach to accurately estimate the Wasserstein distance between datasets, specifically tailored for the generative setting. Instead of employing the commonly used gradient penalty term in the WGAN training procedure, we introduce two objective functions that utilize the $c$-transform based on Kantorovich duality, which is a fundamental property in optimal transport theory. Through our experiments, we observe that this algorithm effectively enforces the Lipschitz constraint on the discriminator, paving the way for understanding the optimal transport problem via a deep learning approach. As a result, our method provides an accurate estimation not only for the optimal discriminator but also for the Wasserstein distance between the true and generated distribution. Notably, our method eliminates the need for gradient penalties and corresponding hyperparameter tuning. Moreover, we demonstrate its effectiveness by generating competitive synthetic images using various datasets such as MNIST, Fashion-MNIST, CIFAR-10, and CelebA-HQ.
Submission Length: Long submission (more than 12 pages of main content)
Changes Since Last Submission: Revised manuscript based on the review.
Assigned Action Editor: ~Ruoyu_Sun1
Submission Number: 2762
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