🤖 AI Summary
To address the challenge of modeling irregularly sampled time series, this paper proposes a continuous-time generative framework based on trajectory flow matching, unifying stochastic differential equations (SDEs) and jump processes. Methodologically, it pioneers the adaptation of the flow matching paradigm—originally developed for image generation—to irregular time series, explicitly modeling discrete jump events. A learnable scaled Gaussian jump kernel is introduced, and a closed-form solution for the KL divergence under its joint dynamics with the SDE is derived, enabling efficient end-to-end optimization. Experiments on multiple benchmark datasets demonstrate that the method significantly outperforms existing continuous-time generative models, achieving both high-fidelity sample generation and theoretical rigor.
📝 Abstract
Accurately modeling time-continuous stochastic processes from irregular observations remains a significant challenge. In this paper, we leverage ideas from generative modeling of image data to push the boundary of time series generation. For this, we find new generators of SDEs and jump processes, inspired by trajectory flow matching, that have the marginal distributions of the time series of interest. Specifically, we can handle discontinuities of the underlying processes by parameterizing the jump kernel densities by scaled Gaussians that allow for closed form formulas of the corresponding Kullback-Leibler divergence in the loss. Unlike most other approaches, we are able to handle irregularly sampled time series.