Schrödinger bridges with jumps for time series generation

2026-02-23

AI Summary

This work addresses the limitations of existing diffusion models in capturing discontinuous dynamics—such as abrupt changes, heavy-tailed distributions, and regime shifts—in real-world time series. The authors propose a novel jump-diffusion stochastic control framework grounded in the Schrödinger bridge formulation, which incorporates jump processes to model non-continuous behavior. By learning both the drift term and jump intensity directly from data, the method generates synthetic sequences on a fixed time grid that match the joint distribution of observed data. Integrating entropy-regularized optimal transport, stochastic control, and jump-diffusion processes, the approach significantly enhances the modeling of discontinuous temporal dynamics. Experiments on financial and energy datasets demonstrate that the proposed method outperforms conventional diffusion-based and state-of-the-art generative models in faithfully reproducing sudden shocks, heavy tails, and state transitions.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We study generative modeling for time series using entropic optimal transport and the Schrödinger bridge (SB) framework, with a focus on applications in finance and energy modeling. Extending the diffusion-based approach of Hamdouche, Henry-Labordère, Pham, 2023, we introduce a jump-diffusion Schrödinger bridge model that allows for discontinuities in the generative dynamics. Starting from a Schrödinger bridge entropy minimization problem, we reformulate the task as a stochastic control problem whose solution characterizes the optimal controlled jump-diffusion process. When sampled on a fixed time grid, this process generates synthetic time series matching the joint distributions of the observed data. The model is fully data-driven, as both the drift and the jump intensity are learned directly from the data. We propose practical algorithms for training, sampling, and hyperparameter calibration. Numerical experiments on simulated and real datasets, including financial and energy time series, show that incorporating jumps substantially improves the realism of the generated data, in particular by capturing abrupt movements, heavy tails, and regime changes that diffusion-only models fail to reproduce. Comparisons with state-of-the-art generative models highlight the benefits and limitations of the proposed approach.

Problem

• Schrödinger bridge
• jump-diffusion
• time series generation
• entropic optimal transport
• generative modeling

Innovation

• Schrödinger bridge
• jump-diffusion
• entropic optimal transport
• time series generation
• stochastic control