mlsanityData to 7 Oct 2026

DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models

arXiv 2301.13629 ↗First posted 31 Jan 2023cs.LGcited by 81

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

Spatio-temporal graph neural networks (STGNN) have emerged as the dominant model for spatio-temporal graph (STG) forecasting. Despite their success, they fail to model intrinsic uncertainties within STG data, which cripples their practicality in downstream tasks for decision-making. To this end, this paper focuses on probabilistic STG forecasting, which is challenging due to the difficulty in modeling uncertainties and complex ST dependencies. In this study, we present the first attempt to generalize the popular denoising diffusion probabilistic models to STGs, leading to a novel non-autoregressive framework called DiffSTG, along with the first denoising network UGnet for STG in the framework. Our approach combines the spatio-temporal learning capabilities of STGNNs with the uncertainty measurements of diffusion models. Extensive experiments validate that DiffSTG reduces the Continuous Ranked Probability Score (CRPS) by 4%-14%, and Root Mean Squared Error (RMSE) by 2%-7% over existing methods on three real-world datasets.

Key facts. Cited by 81 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 37 of its 56 references that are in the map. First posted on arXiv 31 Jan 2023.

Builds on

37 of 56 references.

Closest ancestors · 4

Same direction, newest first

  1. 2022Denoising diffusion probabilistic models for probabilistic energy forecasting6 Dec
  2. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation7 Jul
  3. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting28 Jan
  4. 2020Permutation Invariant Graph Generation via Score-Based Generative Modeling2 Mar

Other references · 33

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  4. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  5. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  6. 2020Denoising Diffusion Implicit Modelscited by 9,655
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  8. 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,141
  9. 2016WaveNet: A Generative Model for Raw Audiocited by 1,710
  10. 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,571
  11. 2018An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modelingcited by 1,447
  12. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
21 more
  1. 2022FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecastingcited by 1,200
  2. 2017Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecastingcited by 1,125
  3. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  4. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,004
  5. 2019Graph WaveNet for Deep Spatial-Temporal Graph Modelingcited by 820
  6. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 620
  7. 2016Recurrent Neural Networks for Multivariate Time Series with Missing Valuescited by 548
  8. 2022Transformers in Time Series: A Surveycited by 489
  9. 2022MCVD: Masked Conditional Video Diffusion for Prediction, Generation, and Interpolationcited by 307
  10. 2020Glow-TTS: A Generative Flow for Text-to-Speech via Monotonic Alignment Searchcited by 269
  11. 2017Concrete Dropoutcited by 227
  12. 2018Deep Multi-View Spatial-Temporal Network for Taxi Demand Predictioncited by 162
  13. 2021DiffSinger: Singing Voice Synthesis via Shallow Diffusion Mechanismcited by 154
  14. 2021Graph Neural Controlled Differential Equations for Traffic Forecastingcited by 133
  15. 2023Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglementcited by 89
  16. 2022AirFormer: Predicting Nationwide Air Quality in China with Transformerscited by 73
  17. 2021Quantifying Uncertainty in Deep Spatiotemporal Forecastingcited by 48
  18. 2022STDEN: Towards Physics-Guided Neural Networks for Traffic Flow Predictioncited by 45
  19. 2021Spatio-temporal graph neural networks for multi-site PV power forecastingcited by 22
  20. 2021RNN with Particle Flow for Probabilistic Spatio-temporal Forecastingcited by 16
  21. 2023A Transformer-based Diffusion Probabilistic Model for Heart Rate and Blood Pressure Forecasting in Intensive Care Unitcited by 14

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 13; 2024: 28; 2025: 27; 2026: 13.

81 papers.

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  1. 2024Foundation Models for Time Series Analysis: A Tutorial and Surveycited by 234
  2. 2023GenCast: Diffusion-based ensemble forecasting for medium-range weathercited by 169
  3. 2023A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detectioncited by 145
  4. 2023Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Surveycited by 140
  5. 2023Large Models for Time Series and Spatio-Temporal Data: A Survey and Outlookcited by 109
  6. 2023Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospectscited by 97
  7. 2024Spatial-Temporal Large Language Model for Traffic Predictioncited by 81
  8. 2023Diffusion Models for Time Series Applications: A Surveycited by 72
  9. 2024A Survey on Diffusion Models for Time Series and Spatio-Temporal Datacited by 66
  10. 2023DiffTraj: Generating GPS Trajectory with Diffusion Probabilistic Modelcited by 64
  11. 2023CARD: Channel Aligned Robust Blend Transformer for Time Series Forecastingcited by 55
  12. 2024ControlTraj: Controllable Trajectory Generation with Topology-Constrained Diffusion Modelcited by 48
38 more
  1. 2023Deciphering Spatio-Temporal Graph Forecasting: A Causal Lens and Treatmentcited by 47
  2. 2024Deep Learning for Cross-Domain Data Fusion in Urban Computing: Taxonomy, Advances, and Outlookcited by 33
  3. 2024Efficient Large-Scale Traffic Forecasting with Transformers: A Spatial Data Management Perspectivecited by 24
  4. 2025Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networkscited by 24
  5. 2025Foundation Models for Spatio-Temporal Data Science: A Tutorial and Surveycited by 23
  6. 2023Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learningcited by 20
  7. 2025T2S: High-resolution Time Series Generation with Text-to-Series Diffusion Modelscited by 19
  8. 2023Graph Neural Processes for Spatio-Temporal Extrapolationcited by 18
  9. 2023Towards Generative Modeling of Urban Flow through Knowledge-enhanced Denoising Diffusioncited by 17
  10. 2024Spatio-Temporal Few-Shot Learning via Diffusive Neural Network Generationcited by 14
  11. 2024Diffusion-Based Environment-Aware Trajectory Predictioncited by 14
  12. 2024A Survey of Generative Techniques for Spatial-Temporal Data Miningcited by 14
  13. 2024Data-Driven Stochastic Closure Modeling via Conditional Diffusion Model and Neural Operatorcited by 12
  14. 2024Elucidating the Design Choice of Probability Paths in Flow Matching for Forecastingcited by 12
  15. 2025Relational Conformal Prediction for Correlated Time Seriescited by 11
  16. 2024Self-Supervised Learning of Time Series Representation via Diffusion Process and Imputation-Interpolation-Forecasting Maskcited by 10
  17. 2024Diffusion Transformers as Open-World Spatiotemporal Foundation Modelscited by 10
  18. 2024A Universal Model for Human Mobility Predictioncited by 10
  19. 2025Unraveling Spatio-Temporal Foundation Models via the Pipeline Lens: A Comprehensive Reviewcited by 10
  20. 2024DiffsFormer: A Diffusion Transformer on Stock Factor Augmentationcited by 9
  21. 2024A Systematic Literature Review of Spatio-Temporal Graph Neural Network Models for Time Series Forecasting and Classificationcited by 9
  22. 2025Vision-Enhanced Time Series Forecasting via Latent Diffusion Modelscited by 9
  23. 2024DiffSTOCK: Probabilistic relational Stock Market Predictions using Diffusion Modelscited by 8
  24. 2025UQGNN: Uncertainty Quantification of Graph Neural Networks for Multivariate Spatiotemporal Predictioncited by 8
  25. 2026HealthMamba: An Uncertainty-aware Spatiotemporal Graph State Space Model for Effective and Reliable Healthcare Facility Visit Predictioncited by 8
  26. 2025Uncertainty-aware Predict-Then-Optimize Framework for Equitable Post-Disaster Power Restorationcited by 7
  27. 2025Causal Time Series Generation via Diffusion Modelscited by 7
  28. 2023A Survey of Generative AI for Intelligent Transportation Systems: Road Transportation Perspectivecited by 6
  29. 2024SpecSTG: A Fast Spectral Diffusion Framework for Probabilistic Spatio-Temporal Traffic Forecastingcited by 5
  30. 2025Graph Signal Generative Diffusion Modelscited by 5
  31. 2025Generative AI for Self-Adaptive Systems: State of the Art and Research Roadmapcited by 5
  32. 2026TrustEnergy: A Unified Framework for Accurate and Reliable User-level Energy Usage Predictioncited by 5
  33. 2024A Temporally Disentangled Contrastive Diffusion Model for Spatiotemporal Imputationcited by 4
  34. 2024A Gentle Introduction and Tutorial on Deep Generative Models in Transportation Researchcited by 4
  35. 2024Towards Kriging-informed Conditional Diffusion for Regional Sea-Level Data Downscalingcited by 4
  36. 2025Unveiling the Power of Noise Priors: Enhancing Diffusion Models for Mobile Traffic Predictioncited by 4
  37. 2025Leveraging the Spatial Hierarchy: Coarse-to-fine Trajectory Generation via Cascaded Hybrid Diffusioncited by 4
  38. 2026Deep Generative Spatiotemporal Engression for Probabilistic Forecasting of Epidemicscited by 4

50 most cited of 81 All 81 (JSON)

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  1. 2023Dynamic Causal Explanation Based Diffusion-Variational Graph Neural Network for Spatio-temporal Forecasting
  2. 2026GARDiff: Graph-Aligned Residual Diffusion for Probabilistic Multivariate Time-Series Forecasting
  3. 2026FaST: Efficient and Effective Long-Horizon Forecasting for Large-Scale Spatial-Temporal Graphs via Mixture-of-Experts
  4. 2025DiffGraph: Heterogeneous Graph Diffusion Model
  5. 2024diffIRM: A Diffusion-Augmented Invariant Risk Minimization Framework for Spatiotemporal Prediction over Graphs
  6. 2024SpoT-Mamba: Learning Long-Range Dependency on Spatio-Temporal Graphs with Selective State Spaces
  7. 2026DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting
  8. 2024STG-Mamba: Spatial-Temporal Graph Learning via Selective State Space Model