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.

翻译：由于复杂的空间依赖性和时间动态性，时空数据的精确预测仍具挑战性。此类数据固有的不确定性和变异性常使确定性模型难以胜任，从而推动了向概率方法的转变，其中基于扩散的生成模型已成为有效的解决方案。本文提出ProGen，一种用于概率时空时间序列预测的新型框架，该框架在连续域中利用随机微分方程和基于扩散的生成建模技术。通过集成一种新颖的去噪分数模型、图神经网络以及一个定制的随机微分方程，ProGen提供了一个稳健的解决方案，能有效捕捉时空依赖性并管理不确定性。我们在四个基准交通数据集上进行的大量实验表明，ProGen的性能优于最先进的确定性和概率模型。这项工作为时空预测贡献了一种连续的、基于扩散的生成方法，为概率建模和随机过程的未来研究铺平了道路。