离散Wasserstein流实现单步生成模型
Discrete Wasserstein Flows for One-Step Generative Modeling
这篇论文提出了离散Wasserstein流框架，实现了单步生成模型，在有限状态空间上解决了传统方法的问题。
研究人员提出了一种有限状态空间上的单步生成模型新框架。该框架使用离散Wasserstein几何定义了可逆马尔可夫核转换上的目标相对KL梯度流。通过马尔可夫跳跃在粒子级别实现这一概率流，并将传输更新摊销到潜在条件生成器中，使迭代动态仅在训练期间需要，推理保持单步。在底层分布和传输动力学可精确计算的受控环境中，验证了KL耗散、粒子动力学与概率流的一致性以及预测的数值缩放。
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 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.
