---
title: "Generative SDEs with Trainable Diffusion and Density-Based Losses"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2610.41243v1"
permalink: "https://feed.astralor.com/items/itm_96f31b8aa6b52e76c51824ef"
published: "2026-10-30T04:35:59.000Z"
score: 49
channel: "ai"
tags: ["Generative SDEs","Trainable Diffusion","Density-Based Losses","SDE","Gaussian","Gaussian-mixture"]
---

# Generative SDEs with Trainable Diffusion and Density-Based Losses

## 速览

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-dime…

## 关键点

- 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.

## 全文

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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