Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models

Yuzhen Zhao; Yating Liu; Quentin Guibert

stat.MLOct 6, 2026

Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models

Authors: Yuzhen Zhao, Yating Liu, Quentin Guibert

Organizations: CEREMADE, CNRS, Universite Paris-Dauphine, PSL, 75016 Paris, France

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.

Figures & tables

Panel of Figure 1 — Figure 1: Comparison of test sample paths with sample paths generated by our method (left) and by the method in Gao et al. (2025) (right).

Panel of Figure 2 — Figure 2: Empirical convergence rates for $d=1$ (left) and $d=2$ (right).

Panel of Figure 3 — Figure 3: Comparison of the empirical convergence rates for sample paths generated by our method and by Gao et al. (2025) for $d=1$ (left) and $d=2$ (right).

Panel of Figure 4 — Figure 4: One-step forecasts of our estimator on the test segment for BTC and ETH in the Crypto dataset (top) and for the Danish dataset (bottom).

Panel of Figure 5 — Figure 5: One-step forecasts of the time-homogeneous SBJTS estimator on the test segment for BTC and ETH in the Crypto dataset (top) and for the Danish dataset (bottom). The curves and the band are constructed as in Figure 4 .

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

$d$	$N$	Our estimator	Estimator of Gao et al. (2025)
$1$	$100$	$0.165\pm 0.093$	$3.265\pm 0.153$
$1$	$200$	$0.140\pm 0.086$	$3.120\pm 0.186$
$1$	$500$	$0.087\pm 0.037$	$3.055\pm 0.127$
$1$	$1000$	$0.095\pm 0.032$	$2.923\pm 0.106$
$1$	$2000$	$0.075\pm 0.033$	$2.685\pm 0.069$
$1$	$5000$	$0.050\pm 0.019$	$2.333\pm 0.065$

Appendix

Table 1: Joint KL estimates (mean

\pm

95\%

CI half-width) for our estimator and the estimator of Gao et al. (2025) .

Panel of Figure 6 — Figure 6: One-step forecasts of our estimator (left) and time-homogeneous SBJTS estimator from De Marco et al. (2026) (right) on the test segment.

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Abstract

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