论文解决了退化扩散模型条件化的难题，提出基于因果最优传输的新方法，适用于传统分数函数失效的场景。
该研究针对条件生成模型在训练过程中过度依赖分数函数的问题。研究聚焦于扩散系数奇异的扩散过程，以及条件密度不存在或不平滑的情况。研究团队使用因果最优传输定义了近似损失函数，在最小假设条件下识别最小熵控制。该方法基于因果最优传输及其通过(条件)扩散过程的可预测表示特性。
Conditioning Degenerate Diffusion Models
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.