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

arXiv: https://arxiv.org/abs/2610.09045 · HTML: https://mlsanity.com/paper/2610.09045/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 1 of its 21 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 1 of 1)

- [Generating solution paths of Markovian stochastic differential equations using diffusion models](https://mlsanity.com/paper/2509.08731/) (2025)

## Abstract (arXiv)

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.