发表机构
University of Illinois Urbana Champaign（伊利诺伊大学厄巴纳-香槟分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对奇异扩散系数且密度不光滑的条件生成模型，该研究提出基于因果最优传输的近似损失函数，以实现最小熵控制的引导。
AI 中文摘要
当前条件生成模型在训练期间严重依赖评分函数作为引导。当生成模型是具有奇异扩散系数的扩散过程，且基础（条件）密度不存在或不光滑时，我们使用因果最优传输来定义近似损失函数，这些函数在最少假设下识别出用于引导的最小熵控制。我们的方法依赖于因果最优传输及其通过（条件）扩散过程的可预测表示性质的表征，该过程的相关鞅问题适定，遵循Üstünel的思路。
英文摘要
Current conditioned generative models heavily rely on score functions for guidance during training. When the generative model is a diffusion process with a singular diffusion coefficient and the underlying (conditional) densities either do not exist or are not smooth, we use causal optimal transport to define \emph{approximate} loss functions that identify a minimum-entropy control for guidance under minimal assumptions. Our approach relies on causal optimal transport and its characterization through the predictable representation property of (conditioned) diffusion processes whose associated martingale problem is well posed, à la Üstünel.
Commentsv2: Fixed typos in the affiliation and citations, and added a new definition in appendix to clarify the terminology
