提出新型生成框架，让模型通过可追踪的潜变量过程生成数据。
Latent Process Generator Matching
- 将生成过程建模为可追踪的马尔可夫潜变量动态过程
- 学习图像空间的生成器，其单时态分布与投影过程一致
- 拓展生成匹配理论，支持时变潜变量条件建模
许多近期基于流匹配和扩散风格的生成模型依赖训练时的辅助随机动态：模拟更丰富的过程以定义条件目标，但辅助状态在生成时要么不可采样，要么并非期望输出。现有生成匹配理论仅形式化静态潜变量的条件，少数论文证明了特定扩展状态构造下的投影结果。本文提出潜过程生成匹配（Latent Process Generator Matching），将观测生成状态建模为可追踪马尔可夫过程 $Y_t$ 的确定性映射 $X_t=Φ(Y_t)$。我们证明在此设定下，可学习图像空间的生成器，使其单时态边缘分布与投影过程相同。该框架广义化并包含已有离散潜变量结果，将生成匹配从静态潜变量推广至一类丰富的时间依赖潜条件过程。
原文摘要 · Abstract (English)
Many recent flow-matching and diffusion-style generative models rely on auxiliary stochastic dynamics during training: a richer process is simulated to define conditional targets, but the auxiliary state is either intractable to sample at generation time or simply not part of the desired output. Existing Generator Matching theory formalises conditioning on static latent random variables, and several recent papers prove special cases of projection results for particular augmented-state constructions. We introduce latent process generator matching, a general framework that treats the observed generative state as a deterministic image $X_t=Φ(Y_t)$ of a tractable Markov process $Y_t$. We show that in this setting one may learn the generator of a stochastic process on the image space which has the same one-time marginal distributions as the projected process. This generalizes and subsumes the discrete latent process results from the literature, and extends Generator Matching from static latent variables to a rich family of time-dependent latent conditional processes.
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