Wasserstein-2 Generative Networks
This work addresses the challenge of efficient and unbiased optimal transport in machine learning, with applications in image processing and domain adaptation, though it appears incremental as it builds on existing methods with a novel regularization approach.
The authors tackled the problem of training optimal transport mappings for the Wasserstein-2 distance by proposing a non-minimax algorithm using input convex neural networks and cycle-consistency regularization, which avoids bias and scales well in high dimensions, and they evaluated it on tasks like image-to-image color transfer and domain adaptation.
We propose a novel end-to-end non-minimax algorithm for training optimal transport mappings for the quadratic cost (Wasserstein-2 distance). The algorithm uses input convex neural networks and a cycle-consistency regularization to approximate Wasserstein-2 distance. In contrast to popular entropic and quadratic regularizers, cycle-consistency does not introduce bias and scales well to high dimensions. From the theoretical side, we estimate the properties of the generative mapping fitted by our algorithm. From the practical side, we evaluate our algorithm on a wide range of tasks: image-to-image color transfer, latent space optimal transport, image-to-image style transfer, and domain adaptation.