Papers › (q,p)-Wasserstein GANs: Comparing Ground Metrics for Wasserstein GANs
(q,p)-Wasserstein GANs: Comparing Ground Metrics for Wasserstein GANs
Anton Mallasto, Jes Frellsen, Wouter Boomsma, Aasa Feragen
Generative Adversial Networks (GANs) have made a major impact in computer vision and machine learning as generative models. Wasserstein GANs (WGANs) brought Optimal Transport (OT) theory into GANs, by minimizing the $1$-Wasserstein distance between model and data distributions as their objective function. Since then, WGANs have gained considerable interest due to their stability and theoretical framework. We contribute to the WGAN literature by introducing the family of (q,p)-Wasserstein GANs, which allow the use of more general p-Wasserstein metrics for p≥1 in the GAN learning procedure. While the method is able to incorporate any cost function as the ground metric, we focus on studying the l^q metrics for q≥1. This is a notable generalization as in the WGAN literature the OT distances are commonly based on the l² ground metric. We demonstrate the effect of different p-Wasserstein distances in two toy examples. Furthermore, we show that the ground metric does make a difference, by comparing different (q,p) pairs on the MNIST and CIFAR-10 datasets. Our experiments demonstrate that changing the ground metric and p can notably improve on the common (q,p) = (2,1) case.
In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Methods
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections