# Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learning

arXiv: https://arxiv.org/abs/2310.17360 · HTML: https://mlsanity.com/paper/2310.17360/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 29 of its 50 references that are in the map.
- First posted on arXiv 26 Oct 2023.

## 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, 29 of 29)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2106.12931/) (2021)
- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [Graph Neural Controlled Differential Equations for Traffic Forecasting](https://mlsanity.com/paper/2112.03558/) (2021)
- [STAN: Spatio-Temporal Attention Network for Next Location Recommendation](https://mlsanity.com/paper/2102.04095/) (2021)
- [Inductive Graph Neural Networks for Spatiotemporal Kriging](https://mlsanity.com/paper/2006.07527/) (2020)
- [DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models](https://mlsanity.com/paper/2301.13629/) (2023)
- [Diffusion Models for Time Series Applications: A Survey](https://mlsanity.com/paper/2305.00624/) (2023)
- [Quantifying Uncertainty in Deep Spatiotemporal Forecasting](https://mlsanity.com/paper/2105.11982/) (2021)
- [Kriging Convolutional Networks](https://mlsanity.com/paper/2306.09463/) (2023)
- [Spatial Aggregation and Temporal Convolution Networks for Real-time Kriging](https://mlsanity.com/paper/2109.12144/) (2021)
- [INCREASE: Inductive Graph Representation Learning for Spatio-Temporal Kriging](https://mlsanity.com/paper/2302.02738/) (2023)
- [Automated Spatio-Temporal Graph Contrastive Learning](https://mlsanity.com/paper/2305.03920/) (2023)
- [Graph Neural Processes for Spatio-Temporal Extrapolation](https://mlsanity.com/paper/2305.18719/) (2023)
- [STUaNet: Understanding uncertainty in spatiotemporal collective human mobility](https://mlsanity.com/paper/2102.06027/) (2021)
- [Data4UrbanMobility: Towards Holistic Data Analytics for Mobility Applications in Urban Regions](https://mlsanity.com/paper/1903.12064/) (2019)
- [Measuring Spatial Subdivisions in Urban Mobility with Mobile Phone Data](https://mlsanity.com/paper/2002.11636/) (2020)

## Built on by (most cited first, 20 of 20)

- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [ControlTraj: Controllable Trajectory Generation with Topology-Constrained Diffusion Model](https://mlsanity.com/paper/2404.15380/) (2024)
- [A Survey of Generative Techniques for Spatial-Temporal Data Mining](https://mlsanity.com/paper/2405.09592/) (2024)
- [Diffusion Transformers as Open-World Spatiotemporal Foundation Models](https://mlsanity.com/paper/2411.12164/) (2024)
- [Unraveling Spatio-Temporal Foundation Models via the Pipeline Lens: A Comprehensive Review](https://mlsanity.com/paper/2506.01364/) (2025)
- [A Systematic Literature Review of Spatio-Temporal Graph Neural Network Models for Time Series Forecasting and Classification](https://mlsanity.com/paper/2410.22377/) (2024)
- [UQGNN: Uncertainty Quantification of Graph Neural Networks for Multivariate Spatiotemporal Prediction](https://mlsanity.com/paper/2508.08551/) (2025)
- [SpecSTG: A Fast Spectral Diffusion Framework for Probabilistic Spatio-Temporal Traffic Forecasting](https://mlsanity.com/paper/2401.08119/) (2024)
- [Graph Signal Generative Diffusion Models](https://mlsanity.com/paper/2509.17250/) (2025)
- [Fine-Grained Traffic Inference from Road to Lane via Spatio-Temporal Graph Node Generation](https://mlsanity.com/paper/2507.19089/) (2025)
- [UrbanMind: Urban Dynamics Prediction with Multifaceted Spatial-Temporal Large Language Models](https://mlsanity.com/paper/2505.11654/) (2025)
- [Generalising Traffic Forecasting to Regions without Traffic Observations](https://mlsanity.com/paper/2508.08947/) (2025)
- [Double-Diffusion: Balancing Speed, Accuracy, and Uncertainty in Probabilistic Forecasting for Urban Sensor Networks](https://mlsanity.com/paper/2506.23053/) (2025)
- [AdaSTI: Conditional Diffusion Models with Adaptive Dependency Modeling for Spatio-Temporal Imputation](https://mlsanity.com/paper/2509.18144/) (2025)
- [Harnessing Rich Multi-Modal Data for Spatial-Temporal Homophily-Embedded Graph Learning Across Domains and Localities](https://mlsanity.com/paper/2512.11178/) (2025)
- [Pattern-Guided Diffusion Models](https://mlsanity.com/paper/2512.13945/) (2025)
- [Learning Spatio-Temporal Foundation Models from Pure Synthetic Data](https://mlsanity.com/paper/2607.16251/) (2026)
- [Graph Representation via Elements of Discrete Morse and Cobordism Theories](https://mlsanity.com/paper/2610.01937/) (2026)

## Abstract (arXiv)

Spatio-temporal graph learning is a fundamental problem in modern urban systems. Existing approaches tackle different tasks independently, tailoring their models to unique task characteristics. These methods, however, fall short of modeling intrinsic uncertainties in the spatio-temporal data. Meanwhile, their specialized designs misalign with the current research efforts toward unifying spatio-temporal graph learning solutions. In this paper, we propose to model these tasks in a unified probabilistic perspective, viewing them as predictions based on conditional information with shared dependencies. Based on this proposal, we introduce Unified Spatio-Temporal Diffusion Models (USTD) to address the tasks uniformly under the uncertainty-aware diffusion framework. USTD is holistically designed, comprising a shared spatio-temporal encoder and attention-based denoising decoders that are task-specific. The encoder, optimized by pre-training strategies, effectively captures conditional spatio-temporal patterns. The decoders, utilizing attention mechanisms, generate predictions by leveraging learned patterns. Opting for forecasting and kriging, the decoders are designed as Spatial Gated Attention (SGA) and Temporal Gated Attention (TGA) for each task, with different emphases on the spatial and temporal dimensions. Combining the advantages of deterministic encoders and probabilistic decoders, USTD achieves state-of-the-art performances compared to both deterministic and probabilistic baselines, while also providing valuable uncertainty estimates.