PreprintarXiv licencearXiv
Generative SDEs with Trainable Diffusion and Density-Based Losses
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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BibTeX
@misc{ni2026generative,
title = {{Generative SDEs with Trainable Diffusion and Density-Based Losses}},
author = {Angxiu Ni},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41243},
eprint = {2610.41243},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41243},
}
RIS
TY - UNPB
TI - Generative SDEs with Trainable Diffusion and Density-Based Losses
AU - Angxiu Ni
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41243
UR - https://arxiv.org/abs/2610.41243
AB - 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.
ER -