Title: Collaborative Deterministic–Probabilistic Forecasting for Diverse Spatiotemporal Systems
Primary area: learning on time series and dynamical systems
Keywords: Spatiotemporal forecasting, probabilistic forecasting, diffusion models

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. we propose \textbf{CoST}, a general forecasting framework that \underline{\textbf{Co}}llaborates deterministic and diffusion models for diverse \underline{\textbf{S}}patio\underline{\textbf{T}}emporal systems.
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, improves accuracy and efficiency, and generalizes across diverse spatiotemporal systems. 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. Code and datasets are available at: \url{https://anonymous.4open.science/r/CoST_17116}.

TL;DR: We propose a collaborative approach that combines a deterministic model and a diffusion model, leveraging their complementary strengths for probabilistic forecasting.