mlsanityData to 7 Oct 2026

Diffusion Models for Time Series Applications: A Survey

arXiv 2305.00624 ↗First posted 1 May 2023cs.LGcited by 72

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

Abstract (arXiv)

Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data, diffusion models are widely used in image, video, and text synthesis nowadays. In recent years, the concept of diffusion has been extended to time series applications, and many powerful models have been developed. Considering the deficiency of a methodical summary and discourse on these models, we provide this survey as an elementary resource for new researchers in this area and also an inspiration to motivate future research. For better understanding, we include an introduction about the basics of diffusion models. Except for this, we primarily focus on diffusion-based methods for time series forecasting, imputation, and generation, and present them respectively in three individual sections. We also compare different methods for the same application and highlight their connections if applicable. Lastly, we conclude the common limitation of diffusion-based methods and highlight potential future research directions.

Key facts. Cited by 72 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 51 of its 64 references that are in the map. First posted on arXiv 1 May 2023.

Builds on

51 of 64 references.

Closest ancestors · 4

Same direction, newest first

  1. 2023PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation20 Feb
  2. 2023DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Models31 Jan
  3. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation7 Jul
  4. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting28 Jan

Other references · 47

  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. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  8. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,424
  9. 2014Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modelingcited by 2,341
  10. 2022Video Diffusion Modelscited by 2,280
  11. 2016WaveNet: A Generative Model for Raw Audiocited by 1,710
  12. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
35 more
  1. 2021Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecastingcited by 1,654
  2. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  3. 2021Cascaded Diffusion Models for High Fidelity Image Generationcited by 1,155
  4. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  5. 2022Diffusion Models in Vision: A Surveycited by 1,008
  6. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,006
  7. 2020NVAE: A Deep Hierarchical Variational Autoencodercited by 635
  8. 2016Recurrent Neural Networks for Multivariate Time Series with Missing Valuescited by 548
  9. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANscited by 515
  10. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
  11. 2022Understanding Diffusion Models: A Unified Perspectivecited by 337
  12. 2017Real-valued (Medical) Time Series Generation with Recurrent Conditional GANscited by 329
  13. 2022Flexible Diffusion Modeling of Long Videoscited by 294
  14. 2018BRITS: Bidirectional Recurrent Imputation for Time Seriescited by 288
  15. 2022Diffusion Probabilistic Modeling for Video Generationcited by 237
  16. 2018Adversarial Audio Synthesiscited by 222
  17. 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 195
  18. 2019GP-VAE: Deep Probabilistic Time Series Imputationcited by 171
  19. 2022It's Raw! Audio Generation with State-Space Modelscited by 171
  20. 2020Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flowscited by 142
  21. 2021TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generationcited by 139
  22. 2021Graph Neural Controlled Differential Equations for Traffic Forecastingcited by 133
  23. 2016C-RNN-GAN: Continuous recurrent neural networks with adversarial trainingcited by 132
  24. 2021Step-unrolled Denoising Autoencoders for Text Generationcited by 102
  25. 2023Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglementcited by 89
  26. 2017Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networkscited by 86
  27. 2020COT-GAN: Generating Sequential Data via Causal Optimal Transportcited by 70
  28. 2022Latent Diffusion Energy-Based Model for Interpretable Text Modelingcited by 67
  29. 2019Neural Empirical Bayescited by 46
  30. 2021ScoreGrad: Multivariate Probabilistic Time Series Forecasting with Continuous Energy-based Generative Modelscited by 42
  31. 2020Uncertainty-Aware Variational-Recurrent Imputation Network for Clinical Time Seriescited by 33
  32. 2020Smoothness and Stability in GANscited by 27
  33. 2023Regular Time-series Generation using SGMcited by 23
  34. 2021Spatio-temporal graph neural networks for multi-site PV power forecastingcited by 22
  35. 2021Learning Disentangled Representations for Time Seriescited by 8

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 9; 2024: 27; 2025: 19; 2026: 17.

72 papers.

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By area:

  1. 2023Functional Flow Matchingcited by 63
  2. 2023On the Design Fundamentals of Diffusion Models: A Surveycited by 59
  3. 2023Enhancing Deep Reinforcement Learning: A Tutorial on Generative Diffusion Models in Network Optimizationcited by 56
  4. 2023ImDiffusion: Imputed Diffusion Models for Multivariate Time Series Anomaly Detectioncited by 38
  5. 2024Time Series Diffusion in the Frequency Domaincited by 35
  6. 2024Gradient-Free Generation for Hard-Constrained Systemscited by 35
  7. 2025Efficient Diffusion Models: A Surveycited by 35
  8. 2024Attacks and Defenses for Generative Diffusion Models: A Comprehensive Surveycited by 32
  9. 2024The Rise of Diffusion Models in Time-Series Forecastingcited by 25
  10. 2024Empowering Time Series Analysis with Foundation Models: A Comprehensive Surveycited by 23
  11. 2023Quantum-Noise-Driven Generative Diffusion Modelscited by 20
  12. 2023Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learningcited by 20
38 more
  1. 2025BRIDGE: Bootstrapping Text to Control Time-Series Generation via Multi-Agent Iterative Optimization and Diffusion Modelingcited by 18
  2. 2024A Survey of Generative Techniques for Spatial-Temporal Data Miningcited by 14
  3. 2024TimeDART: A Diffusion Autoregressive Transformer for Self-Supervised Time Series Representationcited by 14
  4. 2025Diffusion Models for Time Series Forecasting: A Surveycited by 11
  5. 2024DiffsFormer: A Diffusion Transformer on Stock Factor Augmentationcited by 9
  6. 2025Vision-Enhanced Time Series Forecasting via Latent Diffusion Modelscited by 9
  7. 2023Diffusion Methods for Generating Transition Pathscited by 8
  8. 2024Navigating Tabular Data Synthesis Research: Understanding User Needs and Tool Capabilitiescited by 8
  9. 2025Diffusion and Flow Matching Models for Tabular Data: A Surveycited by 8
  10. 2023A Comprehensive Survey on Generative Diffusion Models for Structured Datacited by 7
  11. 2023Boosting Data Analytics With Synthetic Volume Expansioncited by 7
  12. 2025Causal Time Series Generation via Diffusion Modelscited by 7
  13. 2024Vision-Language Synthetic Data Enhances Echocardiography Downstream Taskscited by 6
  14. 2024Diverse Intra- and Inter-Domain Activity Style Fusion for Cross-Person Generalization in Activity Recognitioncited by 6
  15. 2024A Financial Time Series Denoiser Based on Diffusion Modelcited by 6
  16. 2024Trustworthy Text-to-Image Diffusion Models: A Timely and Focused Surveycited by 6
  17. 2024SpecSTG: A Fast Spectral Diffusion Framework for Probabilistic Spatio-Temporal Traffic Forecastingcited by 5
  18. 2025The Alpha-Alternator: Dynamic Adaptation To Varying Noise Levels In Sequences Using The Vendi Score For Improved Robustness and Performancecited by 5
  19. 2024A Temporally Disentangled Contrastive Diffusion Model for Spatiotemporal Imputationcited by 4
  20. 2024FastSTI: A Fast Conditional Pseudo Numerical Diffusion Model for Spatio-temporal Traffic Data Imputationcited by 4
  21. 2025RDIT: Residual-based Diffusion Implicit Models for Probabilistic Time Series Forecastingcited by 4
  22. 2026Expanding the Chaos: Neural Operator for Stochastic (Partial) Differential Equationscited by 4
  23. 2024Alternators For Sequence Modelingcited by 3
  24. 2024Conditional Lagrangian Wasserstein Flow for Time Series Imputationcited by 3
  25. 2025TimeWak: Temporal Chained-Hashing Watermark for Time Series Datacited by 3
  26. 2025T2I-Diff: fMRI Signal Generation via Time-Frequency Image Transform and Classifier-Free Denoising Diffusion Modelscited by 3
  27. 2024Test Code Generation for Telecom Software Systems using Two-Stage Generative Modelcited by 2
  28. 2024Defining 'Good': Evaluation Framework for Synthetic Smart Meter Datacited by 2
  29. 2024Channel-aware Contrastive Conditional Diffusion for Multivariate Probabilistic Time Series Forecastingcited by 2
  30. 2024When Graph Neural Networks Meet Dynamic Mode Decompositioncited by 2
  31. 2025Boundary-enhanced time series data imputation with long-term dependency diffusion modelscited by 2
  32. 2026Diff-MN: Diffusion Parameterized MoE-NCDE for Continuous Time Series Generation with Irregular Observationscited by 2
  33. 2024Review of Data-centric Time Series Analysis from Sample, Feature, and Periodcited by 1
  34. 2024Generalization capabilities and robustness of hybrid models grounded in physics compared to purely deep learning modelscited by 1
  35. 2024A Systematic Evaluation of Generated Time Series and Their Effects in Self-Supervised Pretrainingcited by 1
  36. 2025Generative Distribution Prediction: A Unified Approach to Multimodal Learningcited by 1
  37. 2025Translation from Wearable PPG to 12-Lead ECGcited by 1
  38. 2026Spectral-Aware Text-to-Time Series Generation with Billion-Scale Multimodal Meteorological Datacited by 1

50 most cited of 72 All 72 (JSON)

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  1. 2024A Survey on Diffusion Models for Time Series and Spatio-Temporal Data
  2. 2024Retrieval-Augmented Diffusion Models for Time Series Forecasting
  3. 2024Series-to-Series Diffusion Bridge Model
  4. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization
  5. 2024Generative Diffusion Modeling: A Practical Handbook
  6. 2025DS-Diffusion: Data Style-Guided Diffusion Model for Time-Series Generation
  7. 2024A Comprehensive Survey on Diffusion Models and Their Applications
  8. 2024Theoretical research on generative diffusion models: an overview