This work studies the problem of learning transition kernels for time-homogeneous jump-diffusion processes using conditional diffusion models and establishes 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.
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.
FluxLite is introduced, a lightweight, training-free proposal-control framework for discrete diffusion, identifying a tilted-path coverage factor that governs robustness to score error, together with finite-particle convergence for a fixed controlled Feynman-Kac recursion.
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