Generative SDEs with Trainable Diffusion and Density-Based Losses

Angxiu Ni

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arXiv · 2610.41243

Generative SDEs with Trainable Diffusion and Density-Based Losses

Angxiu Ni

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Abstract

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.

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Angxiu Ni. 2026-10-30. Generative SDEs with Trainable Diffusion and Density-Based Losses. https://arxiv.org/abs/2610.41243

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