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This arXiv preprint proposes a training method for neural stochastic differential equations used as generative models. It jointly learns drift, diffusion, and the initial distribution using losses defined on the terminal density, and reports fewer off-mode samples than score-based baselines on low-dimensional Gaussian-mixture benchmarks. The results are limited to synthetic toy settings with similar parameter counts, so practitioners should treat the gains as preliminary until they are tested on real data and larger models.
Generative SDEs with Trainable Diffusion and Density-Based Losses
arXiv:2610.41243v1 Announce Type: new 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.
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.
Machine Learning (cs.LG); Dynamical Systems (math.DS)
arXiv:2610.41243 [cs.LG]
(or arXiv:2610.41243v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.41243 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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