arXiv：cs.LG（机器学习，全量分类）· Alessandro Micheli, Andrea Zerio, Samir Bhatt·· 1 天前AI 评分35
Discrete Wasserstein Flows：面向一步生成建模的离散漂移框架
Discrete Wasserstein Flows for One-Step Generative Modeling
AI 导读
研究者提出 Discrete Wasserstein Flows 框架，用离散 Wasserstein 几何在可逆马尔可夫核的转移上定义目标相对的 KL 梯度流，实现有限状态空间上的一步生成建模。
正文
Abstract: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.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.01355 [cs.LG] |
| (or arXiv:2610.01355v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.01355 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Andrea Zerio [view email]
[v1]
Thu, 1 Oct 2026 09:25:25 UTC (376 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org