基于密度的损失训练随机微分方程生成模型：联合优化漂移与扩散场
Generative SDEs with Trainable Diffusion and Density-Based Losses
arXiv 上一篇新论文，教神经网络学 SDE 做生成，样本比同参数量的 score-based 方法更少跑偏到错误模式上，做生成模型研究的可以看看。
论文提出 divergence-kernel 方法，用直接依赖终端密度的损失联合优化神经 SDE 的漂移场、扩散场和初始高斯分布。在二维和八维高斯混合实验中，学到的是与时间无关的场。与参数量相近的 score-based 生成器相比，偏离模式的样本数大幅减少。其机制是漂移把样本吸引向各模式，扩散负责在模式之间分散多余概率。
Generative SDEs with Trainable Diffusion and Density-Based Losses
We develop a divergence-kernel method for jointly optimizing neural SDE drift and diffusion fields and the initial Gaussian distribution, using losses that depend directly on the terminal density. In two- and eight-dimensional Gaussian-mixture experiments, we learn time-independent fields and obtain far fewer off-mode samples than score-based generators with similar parameter counts. The drift attracts samples toward the modes, while the diffusion helps disperse excess probability between them.
