Discrete Wasserstein Flows for One-Step Generative Modeling
Discrete Wasserstein flows enable one-step generative modeling on finite state spaces.
The paper introduces one-step generative modeling on finite state spaces using discrete Wasserstein geometry. A target-relative KL gradient flow is defined over transitions of a reversible Markov kernel, realized by Markov jumps, and amortized into a latent-conditioned generator. Iterative transport is used only during training, while inference stays one-step. In a setting where distributions and dynamics are exact, the authors verify KL dissipation, particle-flow consistency, and predicted scaling, and show a finite-capacity network can track the transport targets.
- Defines a KL gradient flow with discrete Wasserstein geometry.
- Markov-jump transport is amortized into a latent-conditioned generator.
- Iterative dynamics are training-only; inference remains one step.
- A finite neural generator tracks exact transport targets.
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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 dynamics and the probability flow, and the predicted numerical scaling. We further show that a finite-capacity neural generator can track these exact transport targets while retaining one-step generation. These results validate the basic construction and provide a foundation for scaling Discrete Drifting to structured discrete data.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2610.01355