# Collaborative Deterministic-Probabilistic Forecasting for Diverse Spatiotemporal Systems

arXiv: https://arxiv.org/abs/2502.11013 · HTML: https://mlsanity.com/paper/2502.11013/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 40 of its 71 references that are in the map.
- First posted on arXiv 16 Feb 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 40)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction](https://mlsanity.com/paper/1610.00081/) (2016)
- [Preserve Your Own Correlation: A Noise Prior for Video Diffusion Models](https://mlsanity.com/paper/2305.10474/) (2023)
- [Spatio-Temporal Graph Transformer Networks for Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2005.08514/) (2020)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [FreeNoise: Tuning-Free Longer Video Diffusion via Noise Rescheduling](https://mlsanity.com/paper/2310.15169/) (2023)
- [Spatial-Temporal Identity: A Simple yet Effective Baseline for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2208.05233/) (2022)
- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [PredRNN++: Towards A Resolution of the Deep-in-Time Dilemma in Spatiotemporal Predictive Learning](https://mlsanity.com/paper/1804.06300/) (2018)
- [Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling](https://mlsanity.com/paper/2309.15214/) (2023)
- [DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting](https://mlsanity.com/paper/2306.01984/) (2023)
- [CARD: Classification and Regression Diffusion Models](https://mlsanity.com/paper/2206.07275/) (2022)
- [PreDiff: Precipitation Nowcasting with Latent Diffusion Models](https://mlsanity.com/paper/2307.10422/) (2023)
- [Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement](https://mlsanity.com/paper/2301.03028/) (2023)
- [UniST: A Prompt-Empowered Universal Model for Urban Spatio-Temporal Prediction](https://mlsanity.com/paper/2402.11838/) (2024)
- [DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models](https://mlsanity.com/paper/2301.13629/) (2023)
- [Non-autoregressive Conditional Diffusion Models for Time Series Prediction](https://mlsanity.com/paper/2306.05043/) (2023)
- [Diffusion Models for Time Series Applications: A Survey](https://mlsanity.com/paper/2305.00624/) (2023)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [DiffCast: A Unified Framework via Residual Diffusion for Precipitation Nowcasting](https://mlsanity.com/paper/2312.06734/) (2023)
- [STG2Seq: Spatial-temporal Graph to Sequence Model for Multi-step Passenger Demand Forecasting](https://mlsanity.com/paper/1905.10069/) (2019)

## Abstract (arXiv)

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 CoST, a general forecasting framework that collaborates deterministic and diffusion models for diverse spatiotemporal 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.