mlsanityData to 7 Oct 2026

ScoreGrad: Multivariate Probabilistic Time Series Forecasting with Continuous Energy-based Generative Models

arXiv 2106.10121 ↗First posted 18 Jun 2021cs.LG stat.MLcited by 42

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Cited by 30 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Multivariate time series prediction has attracted a lot of attention because of its wide applications such as intelligence transportation, AIOps. Generative models have achieved impressive results in time series modeling because they can model data distribution and take noise into consideration. However, many existing works can not be widely used because of the constraints of functional form of generative models or the sensitivity to hyperparameters. In this paper, we propose ScoreGrad, a multivariate probabilistic time series forecasting framework based on continuous energy-based generative models. ScoreGrad is composed of time series feature extraction module and conditional stochastic differential equation based score matching module. The prediction can be achieved by iteratively solving reverse-time SDE. To the best of our knowledge, ScoreGrad is the first continuous energy based generative model used for time series forecasting. Furthermore, ScoreGrad achieves state-of-the-art results on six real-world datasets. The impact of hyperparameters and sampler types on the performance are also explored. Code is available at https://github.com/yantijin/ScoreGradPred.

Key facts. Cited by 42 papers in the map (data through 7 Oct 2026). Builds on 32 of its 51 references that are in the map. First posted on arXiv 18 Jun 2021.

Builds on

32 of 51 references.

References · 32

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2020Denoising Diffusion Implicit Modelscited by 9,655
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  7. 2013Distributed Representations of Words and Phrases and their Compositionalitycited by 3,462
  8. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  9. 2015Variational Inference with Normalizing Flowscited by 2,161
  10. 2016WaveNet: A Generative Model for Raw Audiocited by 1,710
  11. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  12. 2014NICE: Non-linear Independent Components Estimationcited by 1,052
20 more
  1. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  2. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,004
  3. 2017Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networkscited by 869
  4. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  5. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
  6. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecastingcited by 332
  7. 2021How to Train Your Energy-Based Modelscited by 271
  8. 2017A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Predictioncited by 245
  9. 2017A Multi-Horizon Quantile Recurrent Forecastercited by 211
  10. 2019High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processescited by 147
  11. 2020Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flowscited by 142
  12. 2018Temporal Pattern Attention for Multivariate Time Series Forecastingcited by 125
  13. 2017A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learningcited by 107
  14. 2020Residual Energy-Based Models for Text Generationcited by 95
  15. 2019Deep Factors for Forecastingcited by 86
  16. 2017Dilated Recurrent Neural Networkscited by 83
  17. 2019The Randomized Midpoint Method for Log-Concave Samplingcited by 77
  18. 2019GluonTS: Probabilistic Time Series Models in Pythoncited by 45
  19. 2018Learning deep kernels for exponential family densitiescited by 36
  20. 2017Residual LSTM: Design of a Deep Recurrent Architecture for Distant Speech Recognitioncited by 19

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Citing papers per year: 2021: 1; 2022: 2; 2023: 8; 2024: 17; 2025: 6; 2026: 8.

42 papers.

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  3. 2022A Survey on Generative Diffusion Modelcited by 238
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  5. 2023Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglementcited by 89
  6. 2023Diffusion Models for Time Series Applications: A Surveycited by 72
  7. 2024A Survey on Diffusion Models for Time Series and Spatio-Temporal Datacited by 66
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  9. 2024Attacks and Defenses for Generative Diffusion Models: A Comprehensive Surveycited by 32
  10. 2024The Rise of Diffusion Models in Time-Series Forecastingcited by 25
  11. 2023Regular Time-series Generation using SGMcited by 23
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  7. 2023A Comprehensive Survey on Generative Diffusion Models for Structured Datacited by 7
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  9. 2024Constrained Posterior Sampling: Time Series Generation with Hard Constraintscited by 6
  10. 2025Dynamic data generation and dynamic portfolio selection: an application of a score-based diffusion modelcited by 5
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