mlsanityData to 14 Oct 2026

CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation

arXiv 2107.03502 ↗First posted 7 Jul 2021cs.LG stat.MLcited by 582

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

Abstract (arXiv)

The imputation of missing values in time series has many applications in healthcare and finance. While autoregressive models are natural candidates for time series imputation, score-based diffusion models have recently outperformed existing counterparts including autoregressive models in many tasks such as image generation and audio synthesis, and would be promising for time series imputation. In this paper, we propose Conditional Score-based Diffusion models for Imputation (CSDI), a novel time series imputation method that utilizes score-based diffusion models conditioned on observed data. Unlike existing score-based approaches, the conditional diffusion model is explicitly trained for imputation and can exploit correlations between observed values. On healthcare and environmental data, CSDI improves by 40-65% over existing probabilistic imputation methods on popular performance metrics. In addition, deterministic imputation by CSDI reduces the error by 5-20% compared to the state-of-the-art deterministic imputation methods. Furthermore, CSDI can also be applied to time series interpolation and probabilistic forecasting, and is competitive with existing baselines. The code is available at https://github.com/ermongroup/CSDI.

Key facts. Cited by 582 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 30 of its 45 references that are in the map. First posted on arXiv 7 Jul 2021.

Builds on

30 of 45 references.

Closest ancestors · 2

Same direction, newest first

  1. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting28 Jan
  2. 2020Permutation Invariant Graph Generation via Score-Based Generative Modeling2 Mar

Other references · 28

  1. 2017Attention Is All You Needcited by 60,361
  2. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,399
  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. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  7. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  8. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  9. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  10. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,354
  11. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,043
  12. 2017Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networkscited by 879
16 more
  1. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 622
  2. 2018GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Accelerationcited by 609
  3. 2016Recurrent Neural Networks for Multivariate Time Series with Missing Valuescited by 554
  4. 2018Efficient Attention: Attention with Linear Complexitiescited by 368
  5. 2018BRITS: Bidirectional Recurrent Imputation for Time Seriescited by 290
  6. 2021Multi-Time Attention Networks for Irregularly Sampled Time Seriescited by 238
  7. 2020Transformer Hawkes Processcited by 235
  8. 2019GP-VAE: Deep Probabilistic Time Series Imputationcited by 172
  9. 2021Symbolic Music Generation with Diffusion Modelscited by 154
  10. 2019High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processescited by 148
  11. 2020Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flowscited by 144
  12. 2017Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networkscited by 86
  13. 2020Solving Linear Inverse Problems Using the Prior Implicit in a Denoisercited by 79
  14. 2020Uncertainty-Aware Variational-Recurrent Imputation Network for Clinical Time Seriescited by 33
  15. 2021Temporal Latent Auto-Encoder: A Method for Probabilistic Multivariate Time Series Forecastingcited by 32
  16. 2020RDIS: Random Drop Imputation with Self-Training for Incomplete Time Series Datacited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 3; 2022: 33; 2023: 92; 2024: 143; 2025: 160; 2026: 151.

582 papers.

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  1. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,114
  2. 2022eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoiserscited by 931
  3. 2022DiffuSeq: Sequence to Sequence Text Generation with Diffusion Modelscited by 450
  4. 2022TabDDPM: Modelling Tabular Data with Diffusion Modelscited by 377
  5. 2022Flexible Diffusion Modeling of Long Videoscited by 294
  6. 2022A Survey on Generative Diffusion Modelcited by 240
  7. 2022Diffusion models as plug-and-play priorscited by 231
  8. 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 198
  9. 2021Conditional Image Generation with Score-Based Diffusion Modelscited by 197
  10. 2025Sundial: A Family of Highly Capable Time Series Foundation Modelscited by 180
  11. 2022Diffusion Models for Video Prediction and Infillingcited by 135
  12. 2023Leapfrog Diffusion Model for Stochastic Trajectory Predictioncited by 132
38 more
  1. 2022GENIE: Higher-Order Denoising Diffusion Solverscited by 127
  2. 2022Uncovering the Disentanglement Capability in Text-to-Image Diffusion Modelscited by 116
  3. 2023Affordance Diffusion: Synthesizing Hand-Object Interactionscited by 110
  4. 2023DiffiT: Diffusion Vision Transformers for Image Generationcited by 106
  5. 2024Rolling Diffusion Modelscited by 104
  6. 2023DiffCollage: Parallel Generation of Large Content with Diffusion Modelscited by 103
  7. 2023Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospectscited by 99
  8. 2023Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecastingcited by 88
  9. 2022BeLFusion: Latent Diffusion for Behavior-Driven Human Motion Predictioncited by 82
  10. 2023DiffSTG: Probabilistic Spatio-Temporal Graph Forecasting with Denoising Diffusion Modelscited by 81
  11. 2023A Survey on Uncertainty Quantification Methods for Deep Learningcited by 81
  12. 2023Non-autoregressive Conditional Diffusion Models for Time Series Predictioncited by 78
  13. 2022Diffusion models for missing value imputation in tabular datacited by 77
  14. 2022HouseDiffusion: Vector Floorplan Generation via a Diffusion Model with Discrete and Continuous Denoisingcited by 73
  15. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimizationcited by 73
  16. 2023Diffusion Models for Time Series Applications: A Surveycited by 72
  17. 2023Functional Flow Matchingcited by 67
  18. 2024A Survey on Diffusion Models for Time Series and Spatio-Temporal Datacited by 67
  19. 2023PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputationcited by 66
  20. 2022DiffPose: Multi-hypothesis Human Pose Estimation using Diffusion modelscited by 65
  21. 2022Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observationscited by 64
  22. 2023Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Treescited by 62
  23. 2022Conditional Simulation Using Diffusion Schr"odinger Bridgescited by 60
  24. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problemscited by 60
  25. 2024Deep Learning for Multivariate Time Series Imputation: A Surveycited by 57
  26. 2022Efficient Video Prediction via Sparsely Conditioned Flow Matchingcited by 55
  27. 2023On the Constrained Time-Series Generation Problemcited by 54
  28. 2023Spatio-temporal Diffusion Point Processescited by 52
  29. 2022Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Modelscited by 50
  30. 2023ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputationcited by 50
  31. 2022Diffusion Generative Models in Infinite Dimensionscited by 49
  32. 2022Compositional Score Modeling for Simulation-based Inferencecited by 48
  33. 2023Uncovering the Missing Pattern: Unified Framework Towards Trajectory Imputation and Predictioncited by 47
  34. 2024Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecastingcited by 43
  35. 2024Utilizing Image Transforms and Diffusion Models for Generative Modeling of Short and Long Time Seriescited by 43
  36. 2023ImDiffusion: Imputed Diffusion Models for Multivariate Time Series Anomaly Detectioncited by 40
  37. 2022Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusioncited by 39
  38. 2023Infinite-Dimensional Diffusion Modelscited by 39

50 most cited of 582 All 582 (JSON)

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  1. 2025CoSTI: Consistency Models for (a faster) Spatio-Temporal Imputation
  2. 2025MissHDD: Hybrid Deterministic Diffusion for Hetrogeneous Incomplete Data Imputation
  3. 2026Impute-EM: Native Mixed-State Diffusion Models for Heterogeneous Data Imputation
  4. 2024RDPI: A Refine Diffusion Probability Generation Method for Spatiotemporal Data Imputation
  5. 2024DiffPuter: Empowering Diffusion Models for Missing Data Imputation
  6. 2026Informative Missingness to Generate Irregular Clinical Time Series
  7. 2021Maximum Likelihood Training of Score-Based Diffusion Models
  8. 2023Zero-Shot Conditioning of Score-Based Diffusion Models by Neuro-Symbolic Constraints