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

Key points

• 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.1
• 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).1
• We then apply our method to real-world data and investigate its performance on a probabilistic forecasting task.1

Sources (1)

• [1]Learning Transition Kernels of Jump-Diffusion Processes with Conditional Diffusion Models
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 6, 07:48 PM

  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.

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