mlsanityData to 14 Oct 2026

Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting

arXiv 2101.12072 ↗First posted 28 Jan 2021cs.LG cs.AIcited by 337

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

Abstract (arXiv)

In this work, we propose textttTimeGrad, an autoregressive model for multivariate probabilistic time series forecasting which samples from the data distribution at each time step by estimating its gradient. To this end, we use diffusion probabilistic models, a class of latent variable models closely connected to score matching and energy-based methods. Our model learns gradients by optimizing a variational bound on the data likelihood and at inference time converts white noise into a sample of the distribution of interest through a Markov chain using Langevin sampling. We demonstrate experimentally that the proposed autoregressive denoising diffusion model is the new state-of-the-art multivariate probabilistic forecasting method on real-world data sets with thousands of correlated dimensions. We hope that this method is a useful tool for practitioners and lays the foundation for future research in this area.

Key facts. Cited by 337 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 33 of its 58 references that are in the map. First posted on arXiv 28 Jan 2021.

Builds on

33 of 58 references.

Closest ancestors · 1

Same direction, newest first

  1. 2020Permutation Invariant Graph Generation via Score-Based Generative Modeling2 Mar

Other references · 32

  1. 2017Attention Is All You Needcited by 60,361
  2. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  3. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  4. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  5. 2020Denoising Diffusion Implicit Modelscited by 9,781
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  8. 2014Sequence to Sequence Learning with Neural Networkscited by 2,986
  9. 2014Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modelingcited by 2,367
  10. 2016Density estimation using Real NVPcited by 2,042
  11. 2016WaveNet: A Generative Model for Raw Audiocited by 1,722
  12. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,354
20 more
  1. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
  2. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,043
  3. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,013
  4. 2019An Introduction to Variational Autoencoderscited by 1,000
  5. 2017Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networkscited by 879
  6. 2016Conditional Image Generation with PixelCNN Decoderscited by 862
  7. 2016Pixel Recurrent Neural Networkscited by 816
  8. 2019N-BEATS: Neural basis expansion analysis for interpretable time series forecastingcited by 753
  9. 2017Masked Autoregressive Flow for Density Estimationcited by 684
  10. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 622
  11. 2019Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecastingcited by 607
  12. 2013Generating Sequences With Recurrent Neural Networkscited by 554
  13. 2018Do Deep Generative Models Know What They Don't Know?cited by 443
  14. 2015A note on the evaluation of generative modelscited by 292
  15. 2021How to Train Your Energy-Based Modelscited by 274
  16. 2019High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processescited by 148
  17. 2020Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flowscited by 144
  18. 2017A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learningcited by 107
  19. 2017Deep and Confident Prediction for Time Series at Ubercited by 50
  20. 2015Artificial Neural Networks Applied to Taxi Destination Predictioncited by 18

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 6; 2022: 32; 2023: 78; 2024: 63; 2025: 72; 2026: 86.

337 papers.

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  1. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,114
  2. 2024Chronos: Learning the Language of Time Seriescited by 759
  3. 2024Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusioncited by 681
  4. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 582
  5. 2022Executing your Commands via Motion Diffusion in Latent Spacecited by 575
  6. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Modelscited by 334
  7. 2022A Survey on Generative Diffusion Modelcited by 240
  8. 2022Diffusion Probabilistic Modeling for Video Generationcited by 238
  9. 2023Implicit Diffusion Models for Continuous Super-Resolutioncited by 218
  10. 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 198
  11. 2025Chronos-2: From Univariate to Universal Forecastingcited by 194
  12. 2023GenCast: Diffusion-based ensemble forecasting for medium-range weathercited by 177
38 more
  1. 2023Leapfrog Diffusion Model for Stochastic Trajectory Predictioncited by 132
  2. 2023AR-Diffusion: Auto-Regressive Diffusion Model for Text Generationcited by 118
  3. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecastingcited by 109
  4. 2023Elucidating the Exposure Bias in Diffusion Modelscited by 101
  5. 2023Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospectscited by 99
  6. 2021Noise Estimation for Generative Diffusion Modelscited by 94
  7. 2023Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglementcited by 90
  8. 2023Input Perturbation Reduces Exposure Bias in Diffusion Modelscited by 90
  9. 2023Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecastingcited by 88
  10. 2022Estimating the Optimal Covariance with Imperfect Mean in Diffusion Probabilistic Modelscited by 83
  11. 2022BeLFusion: Latent Diffusion for Behavior-Driven Human Motion Predictioncited by 82
  12. 2023DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Modelscited by 81
  13. 2023Non-autoregressive Conditional Diffusion Models for Time Series Predictioncited by 78
  14. 2022Diffusion models for missing value imputation in tabular datacited by 77
  15. 2023Diffusion Models for Time Series Applications: A Surveycited by 72
  16. 2023On the Generalization Properties of Diffusion Modelscited by 68
  17. 2023Functional Flow Matchingcited by 67
  18. 2024A Survey on Diffusion Models for Time Series and Spatio-Temporal Datacited by 67
  19. 2022MagicMix: Semantic Mixing with Diffusion Modelscited by 63
  20. 2023DiffCast: A Unified Framework via Residual Diffusion for Precipitation Nowcastingcited by 61
  21. 2021PSA-GAN: Progressive Self Attention GANs for Synthetic Time Seriescited by 58
  22. 2023On the Constrained Time-Series Generation Problemcited by 54
  23. 2023Spatio-temporal Diffusion Point Processescited by 52
  24. 2022Diffusion Generative Models in Infinite Dimensionscited by 49
  25. 2024Retrieval Augmented Time Series Forecastingcited by 46
  26. 2021ScoreGrad: Multivariate Probabilistic Time Series Forecasting with Continuous Energy-based Generative Modelscited by 43
  27. 2024Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecastingcited by 43
  28. 2023ImDiffusion: Imputed Diffusion Models for Multivariate Time Series Anomaly Detectioncited by 40
  29. 2022Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusioncited by 39
  30. 2024Retrieval-Augmented Diffusion Models for Time Series Forecastingcited by 39
  31. 2022Deep Latent State Space Models for Time-Series Generationcited by 38
  32. 2023AlignDiff: Aligning Diverse Human Preferences via Behavior-Customisable Diffusion Modelcited by 37
  33. 2023ProbTS: Benchmarking Point and Distributional Forecasting across Diverse Prediction Horizonscited by 36
  34. 2024TimeDiT: General-purpose Diffusion Transformers for Time Series Foundation Modelcited by 33
  35. 2024MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Processcited by 32
  36. 2022Exploring Generative Neural Temporal Point Processcited by 30
  37. 2022SOS: Score-based Oversampling for Tabular Datacited by 29
  38. 2025Aurora: Towards Universal Generative Multimodal Time Series Forecastingcited by 29

50 most cited of 337 All 337 (JSON)

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  1. 2025Non-stationary Diffusion For Probabilistic Time Series Forecasting
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  3. 2023Add and Thin: Diffusion for Temporal Point Processes
  4. 2026GARDiff: Graph-Aligned Residual Diffusion for Probabilistic Multivariate Time-Series Forecasting
  5. 2025NoiseAR: AutoRegressing Initial Noise Prior for Diffusion Models
  6. 2025Multi-scale Autoregressive Models are Laplacian, Discrete, and Latent Diffusion Models in Disguise
  7. 2024Auto-Regressive Moving Diffusion Models for Time Series Forecasting
  8. 2026StaTS: Spectral Trajectory Schedule Learning for Adaptive Time Series Forecasting with Frequency Guided Denoiser