Discrete Wasserstein Flows for One-Step Generative Modeling

TL;DR

This paper introduces Discrete Wasserstein Flows for one-step generative modeling on finite state spaces. It extends drifting beyond continuous domains using discrete Wasserstein geometry. The method enables one-step generation while retaining iterative dynamics during training.

Why It Matters

The proposed framework has practical significance in generative modeling for discrete data, such as text, graphs, or images. It can be used for efficient and scalable generation of high-quality samples. This can lead to applications in data augmentation, style transfer, and image synthesis.

Key Findings

• KL dissipation verification
• consistency between particle dynamics and probability flow
• finite-capacity neural generator tracking exact transport targets