Collaborative Deterministic-Probabilistic Forecasting for Real-World Spatiotemporal Systems

Abstract: Probabilistic forecasting is crucial for real-world spatiotemporal systems, such as climate, energy, and urban environments, where quantifying uncertainty is essential for informed, risk-aware decision-making. While diffusion models have shown promise in capturing complex data distributions, their application to spatiotemporal forecasting remains limited due to complex spatiotemporal dynamics and high computational demands. In this work, we propose CoST, a novel framework that collaborates deterministic and diffusion models for spatiotemporal forecasting. CoST formulates a mean-residual decomposition strategy: it leverages a powerful deterministic model to capture the conditional mean and a lightweight diffusion model to learn residual uncertainties. This collaborative formulation simplifies learning objectives, enhances forecasting accuracy, enables uncertainty quantification, and significantly improves computational efficiency. To address spatial heterogeneity, we further design a scale-aware diffusion mechanism to guide the diffusion process. Extensive experiments across ten real-world datasets from climate, energy, communication, and urban systems show that CoST achieves 25% performance gains over state-of-the-art baselines, while significantly reducing computational cost.