arXiv：cs.LG· Yuzhen Zhao, Yating Liu, Quentin Guibert·· 4 小时前AI 评分30
用条件扩散模型学习跳跃扩散过程的转移核
Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models
AI 导读
研究提出用条件扩散模型学习时间齐次跳跃扩散过程的转移核，可从N条高频离散时间网格上观测的独立轨迹中生成新样本路径。理论方面给出了条件分数估计误差以及真实路径与生成路径分布间KL散度的非渐近界；数值上先在合成数据上验证理论并与Gao et al. (2025)对比，再应用于真实数据的概率预测任务。
正文
Abstract:We study the problem of learning transition kernels for time-homogeneous jump-diffusion processes using conditional diffusion models, with the goal of generating new sample paths from training data consisting of N independent trajectories observed on a high-frequency discrete time grid. On the theoretical side, we establish non-asymptotic bounds for the conditional score estimation error and for the KL divergence between the laws of the true and generated discretely observed paths. On the numerical side, we first evaluate our method on synthetic data to assess the theoretical findings and benchmark its performance against the approach of Gao et al. (2025). We then apply our method to real-world data and investigate its performance on a probabilistic forecasting task.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.09045 [stat.ML] |
| (or arXiv:2610.09045v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.09045 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Yating Liu [view email]
[v1]
Tue, 6 Oct 2026 19:48:03 UTC (2,411 KB)
来源：arXiv：cs.LG · arxiv.org