Accurate prediction of urban spatiotemporal dynamics is essential for enhancing urban management and decision-making. Existing spatiotemporal prediction models are predominantly deterministic, focusing on primary spatiotemporal patterns. However, those dynamics are highly complex, exhibiting multi-modal distributions that are challenging for deterministic models to capture. In this paper, we highlight the critical role of probabilistic prediction in capturing the uncertainties and complexities inherent in spatiotemporal data. While mainstream probabilistic models can capture uncertainty, they struggle with accurately learning primary patterns and often suffer from computational inefficiency. To address these challenges, we propose CoST, which collaborates deterministic and probabilistic models to improve both predictive accuracy and the ability to handle uncertainty. To achieve this, we design a mean-residual decomposition framework, where the mean value is modeled by a deterministic model, and the residual variations are learned by a probabilistic model, specifically diffusion models. Moreover, we introduce a scale-aware diffusion process, which better accounts for spatially heterogeneous dynamics across different regions. Extensive experiments on eight real-world datasets demonstrate that CoST significantly outperforms existing methods in both deterministic and probabilistic metrics, achieving a 20% improvement with low computational cost. CoST bridges the gap between deterministic precision and probabilistic uncertainty, making a significant advancement in the field of urban spatiotemporal prediction.
View on arXiv@article{sheng2025_2502.11013,
title={ Collaborative Deterministic-Diffusion Model for Probabilistic Spatiotemporal Prediction },
author={ Zhi Sheng and Yuan Yuan and Yudi Zhang and Depeng Jin and Yong Li },
journal={arXiv preprint arXiv:2502.11013},
year={ 2025 }
}