Wasserstein Geodesic Generator for Conditional Distributions

TL;DR

This paper introduces a novel conditional generation method based on Wasserstein geodesics, enabling interpolation between distributions and improved sample generation for tasks like face image synthesis under varying lighting conditions.

Contribution

It derives a tractable upper bound for Wasserstein distance between conditional distributions and proposes the Wasserstein geodesic generator leveraging optimal transport theory.

Findings

Effective interpolation of face images under different lighting conditions.

The method accurately learns conditional distributions and transport maps.

Demonstrates superior performance on face image datasets.

Abstract

Generating samples given a specific label requires estimating conditional distributions. We derive a tractable upper bound of the Wasserstein distance between conditional distributions to lay the theoretical groundwork to learn conditional distributions. Based on this result, we propose a novel conditional generation algorithm where conditional distributions are fully characterized by a metric space defined by a statistical distance. We employ optimal transport theory to propose the Wasserstein geodesic generator, a new conditional generator that learns the Wasserstein geodesic. The proposed method learns both conditional distributions for observed domains and optimal transport maps between them. The conditional distributions given unobserved intermediate domains are on the Wasserstein geodesic between conditional distributions given two observed domain labels. Experiments on face images with light conditions as domain labels demonstrate the efficacy of the proposed method.