Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models
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.
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BibTeX
@misc{zhao2026learning,
title = {{Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models}},
author = {Yuzhen Zhao and Yating Liu and Quentin Guibert},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09045},
eprint = {2610.09045},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05781965v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models
AU - Yuzhen Zhao
AU - Yating Liu
AU - Quentin Guibert
PY - 2026
DA - 2026/10/06
PB - HAL
DO - 10.48550/arxiv.2610.09045
UR - https://hal.science/hal-05781965v1
AB - 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.
ER -