Discrete Wasserstein Flows for One-Step Generative Modeling
We introduce a new framework for one-step generative modelling on finite state spaces. To extend drifting beyond continuous domains, we use discrete Wasserstein geometry to define a target-relative KL gradient flow over the transitions of a reversible Markov kernel. We realize this probability flow at the particle level through Markov jumps and amortize the resulting transport updates into a latent-conditioned generator, so that the iterative dynamics are required only during training while inference remains one-step. In a controlled setting where the underlying distributions and transport dynamics can be computed exactly, we verify KL dissipation, consistency between the particle dynamic...
| Authors | Alessandro Micheli, Andrea Zerio, Samir Bhatt |
|---|---|
| Primary category | cs.LG |
| Published | 1 October 2026 |
| Last updated at source | 1 October 2026 |
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