mlsanityData to 14 Oct 2026

Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows

arXiv 2002.06103 ↗First posted 14 Feb 2020cs.LG stat.MLcited by 144

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Cited by 25 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Time series forecasting is often fundamental to scientific and engineering problems and enables decision making. With ever increasing data set sizes, a trivial solution to scale up predictions is to assume independence between interacting time series. However, modeling statistical dependencies can improve accuracy and enable analysis of interaction effects. Deep learning methods are well suited for this problem, but multivariate models often assume a simple parametric distribution and do not scale to high dimensions. In this work we model the multivariate temporal dynamics of time series via an autoregressive deep learning model, where the data distribution is represented by a conditioned normalizing flow. This combination retains the power of autoregressive models, such as good performance in extrapolation into the future, with the flexibility of flows as a general purpose high-dimensional distribution model, while remaining computationally tractable. We show that it improves over the state-of-the-art for standard metrics on many real-world data sets with several thousand interacting time-series.

Key facts. Cited by 144 papers in the map (data through 14 Oct 2026). First posted on arXiv 14 Feb 2020.

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Citing papers per year: 2021: 14; 2022: 23; 2023: 36; 2024: 27; 2025: 23; 2026: 21.

144 papers.

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  1. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,114
  2. 2024Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusioncited by 681
  3. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 582
  4. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecastingcited by 337
  5. 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 198
  6. 2023Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecastingcited by 113
  7. 2023Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecastingcited by 88
  8. 2023Diffusion Models for Time Series Applications: A Surveycited by 72
  9. 2023Functional Flow Matchingcited by 67
  10. 2021ScoreGrad: Multivariate Probabilistic Time Series Forecasting with Continuous Energy-based Generative Modelscited by 43
  11. 2024Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecastingcited by 43
  12. 2022Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Seriescited by 42
38 more
  1. 2022Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusioncited by 39
  2. 2022TACTiS: Transformer-Attentional Copulas for Time Seriescited by 38
  3. 2023Deep networks for system identification: a Surveycited by 37
  4. 2023ProbTS: Benchmarking Point and Distributional Forecasting across Diverse Prediction Horizonscited by 36
  5. 2021Temporal Latent Auto-Encoder: A Method for Probabilistic Multivariate Time Series Forecastingcited by 32
  6. 2024MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Processcited by 32
  7. 2024Attacks and Defenses for Generative Diffusion Models: A Comprehensive Surveycited by 32
  8. 2025Aurora: Towards Universal Generative Multimodal Time Series Forecastingcited by 29
  9. 2023TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Seriescited by 26
  10. 2023Pushing the Limits of Pre-training for Time Series Forecasting in the CloudOps Domaincited by 23
  11. 2023DiffMotion: Speech-Driven Gesture Synthesis Using Denoising Diffusion Modelcited by 22
  12. 2022Detecting Multivariate Time Series Anomalies with Zero Known Labelcited by 21
  13. 2022Multivariate Time Series Forecasting with Latent Graph Inferencecited by 20
  14. 2024Graph Mixture of Experts and Memory-augmented Routers for Multivariate Time Series Anomaly Detectioncited by 20
  15. 2022Multivariate Quantile Function Forecastercited by 19
  16. 2022Multi-scale Attention Flow for Probabilistic Time Series Forecastingcited by 19
  17. 2021Adjusting for Autocorrelated Errors in Neural Networks for Time Seriescited by 18
  18. 2024SSD-TS: Exploring the Potential of Linear State Space Models for Diffusion Models in Time Series Imputationcited by 18
  19. 2023Nominality Score Conditioned Time Series Anomaly Detection by Point/Sequential Reconstructioncited by 17
  20. 2021RNN with Particle Flow for Probabilistic Spatio-temporal Forecastingcited by 16
  21. 2023pTSE: A Multi-model Ensemble Method for Probabilistic Time Series Forecastingcited by 16
  22. 2023Diffusion Models in Bioinformatics: A New Wave of Deep Learning Revolution in Actioncited by 15
  23. 2021Variance Reduced Training with Stratified Sampling for Forecasting Modelscited by 14
  24. 2022Multivariate Probabilistic Forecasting of Intraday Electricity Prices using Normalizing Flowscited by 14
  25. 2023Conditional Generators for Limit Order Book Environments: Explainability, Challenges, and Robustnesscited by 14
  26. 2023Diffusion-SS3D: Diffusion Model for Semi-supervised 3D Object Detectioncited by 14
  27. 2023Label-Free Multivariate Time Series Anomaly Detectioncited by 14
  28. 2023Deep Learning based Forecasting: a case study from the online fashion industrycited by 12
  29. 2021Deep Time Series Forecasting with Shape and Temporal Criteriacited by 10
  30. 2024Self-Supervised Learning of Time Series Representation via Diffusion Process and Imputation-Interpolation-Forecasting Maskcited by 10
  31. 2025From Samples to Scenarios: A New Paradigm for Probabilistic Forecastingcited by 10
  32. 2023Transport with Support: Data-Conditional Diffusion Bridgescited by 9
  33. 2025Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Modelscited by 9
  34. 2025Probabilistic Forecasting via Autoregressive Flow Matchingcited by 9
  35. 2023Targeted Attacks on Timeseries Forecastingcited by 8
  36. 2025K2VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecastingcited by 8
  37. 2022Random Noise vs State-of-the-Art Probabilistic Forecasting Methods : A Case Study on CRPS-Sum Discrimination Abilitycited by 7
  38. 2022Taming the Long Tail of Deep Probabilistic Forecastingcited by 7

50 most cited of 144 All 144 (JSON)