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.
Keywords
Publication details
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Cite this article
APA 7
Zhao, Y., Liu, Y., & Guibert, Q. (2026). Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models. https://omanscience.com/en/articles/learning-transition-kernels-of-jump-diffusion-processes-with-conditional-diffusion-models
MLA 9
Zhao, Yuzhen, et al. "Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models." https://omanscience.com/en/articles/learning-transition-kernels-of-jump-diffusion-processes-with-conditional-diffusion-models.
Chicago (author–date)
Zhao, Yuzhen, Yating Liu, and Quentin Guibert. 2026. "Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models." https://omanscience.com/en/articles/learning-transition-kernels-of-jump-diffusion-processes-with-conditional-diffusion-models.
Harvard
Zhao, Y., Liu, Y. and Guibert, Q. (2026) 'Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models', Available at: https://omanscience.com/en/articles/learning-transition-kernels-of-jump-diffusion-processes-with-conditional-diffusion-models.
Vancouver
Zhao Y, Liu Y, Guibert Q. Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models. https://omanscience.com/en/articles/learning-transition-kernels-of-jump-diffusion-processes-with-conditional-diffusion-models
IEEE
Y. Zhao, Y. Liu, and Q. Guibert, "Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models," https://omanscience.com/en/articles/learning-transition-kernels-of-jump-diffusion-processes-with-conditional-diffusion-models.