ProGen: Revisiting Probabilistic Spatial-Temporal Time Series Forecasting from a Continuous Generative Perspective Using Stochastic Differential Equations

Abstract: Accurate forecasting of spatiotemporal data remains challenging due to complex spatial dependencies and temporal dynamics. The inherent uncertainty and variability in such data often render deterministic models insufficient, prompting a shift towards probabilistic approaches, where diffusion-based generative models have emerged as effective solutions. In this paper, we present ProGen, a novel framework for probabilistic spatiotemporal time series forecasting that leverages Stochastic Differential Equations (SDEs) and diffusion-based generative modeling techniques in the continuous domain. By integrating a novel denoising score model, graph neural networks, and a tailored SDE, ProGen provides a robust solution that effectively captures spatiotemporal dependencies while managing uncertainty. Our extensive experiments on four benchmark traffic datasets demonstrate that ProGen outperforms state-of-the-art deterministic and probabilistic models. This work contributes a continuous, diffusion-based generative approach to spatiotemporal forecasting, paving the way for future research in probabilistic modeling and stochastic processes.