Wasserstein Geodesic Generator for Conditional Distributions
This work addresses conditional generation for domain-specific applications like image processing, though it appears incremental as it builds on existing optimal transport theory.
The paper tackles the problem of generating samples for specific labels by estimating conditional distributions, proposing a Wasserstein geodesic generator that learns both conditional distributions for observed domains and optimal transport maps between them, with experiments on face images showing its efficacy.
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.