Discrete Wasserstein Flows for One-Step Generative Modeling

The paper presents a new one‑step generative modeling framework for finite state spaces, leveraging discrete Wasserstein geometry to define a target‑relative KL gradient flow over a reversible Markov kernel. The authors implement this flow at the particle level using Markov jumps and encode the resulting transport updates into a latent‑conditioned generator, enabling one‑step inference after training. Experiments on a controlled setting confirm KL dissipation, consistency between particle dynamics and probability flow, and accurate numerical scaling, while a finite‑capacity neural generator successfully tracks the exact transport targets.

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