mlsanityData to 13 Oct 2026

Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models

arXiv 2208.09399 ↗First posted 19 Aug 2022cs.LG stat.MLcited by 195

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Cited by 113 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

The imputation of missing values represents a significant obstacle for many real-world data analysis pipelines. Here, we focus on time series data and put forward SSSD, an imputation model that relies on two emerging technologies, (conditional) diffusion models as state-of-the-art generative models and structured state space models as internal model architecture, which are particularly suited to capture long-term dependencies in time series data. We demonstrate that SSSD matches or even exceeds state-of-the-art probabilistic imputation and forecasting performance on a broad range of data sets and different missingness scenarios, including the challenging blackout-missing scenarios, where prior approaches failed to provide meaningful results.

Key facts. Cited by 195 papers in the map (data through 13 Oct 2026). Builds on 45 of its 68 references that are in the map. First posted on arXiv 19 Aug 2022.

Builds on

45 of 68 references.

References · 45

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,952
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,028
  3. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,213
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,023
  5. 2014Neural Machine Translation by Jointly Learning to Align and Translatecited by 4,539
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,077
  7. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,440
  8. 2022Video Diffusion Modelscited by 2,293
  9. 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,157
  10. 2021Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecastingcited by 1,665
  11. 2020Reformer: The Efficient Transformercited by 1,662
  12. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,425
33 more
  1. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,348
  2. 2021Palette: Image-to-Image Diffusion Modelscited by 1,298
  3. 2021Cascaded Diffusion Models for High Fidelity Image Generationcited by 1,159
  4. 2017Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networkscited by 874
  5. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 621
  6. 2019Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecastingcited by 607
  7. 2020HiPPO: Recurrent Memory with Optimal Polynomial Projectionscited by 602
  8. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 579
  9. 2016Recurrent Neural Networks for Multivariate Time Series with Missing Valuescited by 552
  10. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecastingcited by 335
  11. 2018BRITS: Bidirectional Recurrent Imputation for Time Seriescited by 289
  12. 2022Diffusion Probabilistic Modeling for Video Generationcited by 238
  13. 2020Explaining by Removing: A Unified Framework for Model Explanationcited by 218
  14. 2019GP-VAE: Deep Probabilistic Time Series Imputationcited by 171
  15. 2022It's Raw! Audio Generation with State-Space Modelscited by 171
  16. 2022SAITS: Self-Attention-based Imputation for Time Seriescited by 168
  17. 2015Deep Kalman Filterscited by 165
  18. 2019High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processescited by 147
  19. 2020Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flowscited by 143
  20. 2020Neural Rough Differential Equations for Long Time Seriescited by 142
  21. 2022How to Train Your HiPPO: State Space Models with Generalized Orthogonal Basis Projectionscited by 121
  22. 2017A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learningcited by 107
  23. 2022DiffuseVAE: Efficient, Controllable and High-Fidelity Generation from Low-Dimensional Latentscited by 103
  24. 2021Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networkscited by 94
  25. 2017Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networkscited by 86
  26. 2019Deep Factors for Forecastingcited by 86
  27. 2019NAOMI: Non-Autoregressive Multiresolution Sequence Imputationcited by 59
  28. 2021Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputationcited by 35
  29. 2020Time Series Data Imputation: A Survey on Deep Learning Approachescited by 34
  30. 2021Temporal Latent Auto-Encoder: A Method for Probabilistic Multivariate Time Series Forecastingcited by 32
  31. 2021Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecastingcited by 29
  32. 2021NRTSI: Non-Recurrent Time Series Imputationcited by 25
  33. 2022Classification of datasets with imputed missing values: does imputation quality matter?cited by 21

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2022: 5; 2023: 31; 2024: 63; 2025: 50; 2026: 46.

195 papers.

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  1. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,112
  2. 2022A Survey on Generative Diffusion Modelcited by 240
  3. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecastingcited by 107
  4. 2023Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospectscited by 98
  5. 2023Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecastingcited by 86
  6. 2023Non-autoregressive Conditional Diffusion Models for Time Series Predictioncited by 77
  7. 2023Diffusion Models for Time Series Applications: A Surveycited by 72
  8. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimizationcited by 72
  9. 2024A Survey on Diffusion Models for Time Series and Spatio-Temporal Datacited by 66
  10. 2024Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theorycited by 60
  11. 2024Deep Learning for Multivariate Time Series Imputation: A Surveycited by 57
  12. 2023Effectively Modeling Time Series with Simple Discrete State Spacescited by 54
38 more
  1. 2022Diffusion Generative Models in Infinite Dimensionscited by 49
  2. 2024Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecastingcited by 41
  3. 2024Time Weaver: A Conditional Time Series Generation Modelcited by 36
  4. 2024Retrieval-Augmented Diffusion Models for Time Series Forecastingcited by 36
  5. 2023Diffusion-based Conditional ECG Generation with Structured State Space Modelscited by 35
  6. 2024Stochastic Runge-Kutta Methods: Provable Acceleration of Diffusion Modelscited by 35
  7. 2024TSI-Bench: Benchmarking Time Series Imputationcited by 33
  8. 2024Variational Diffusion Posterior Sampling with Midpoint Guidancecited by 32
  9. 2023SpectralDiff: A Generative Framework for Hyperspectral Image Classification with Diffusion Modelscited by 28
  10. 2023TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Seriescited by 26
  11. 2024The Rise of Diffusion Models in Time-Series Forecastingcited by 25
  12. 2025Non-stationary Diffusion For Probabilistic Time Series Forecastingcited by 24
  13. 2023Add and Thin: Diffusion for Temporal Point Processescited by 22
  14. 2024FlowTS: Time Series Generation via Rectified Flowcited by 22
  15. 2023Quantum-Noise-Driven Generative Diffusion Modelscited by 20
  16. 2024Sports-Traj: A Unified Trajectory Generation Model for Multi-Agent Movement in Sportscited by 19
  17. 2023Binary Latent Diffusioncited by 18
  18. 2024SSD-TS: Exploring the Potential of Linear State Space Models for Diffusion Models in Time Series Imputationcited by 18
  19. 2025BRIDGE: Bootstrapping Text to Control Time-Series Generation via Multi-Agent Iterative Optimization and Diffusion Modelingcited by 18
  20. 2023Diff-E: Diffusion-based Learning for Decoding Imagined Speech EEGcited by 17
  21. 2025Taking a Big Step: Large Learning Rates in Denoising Score Matching Prevent Memorizationcited by 17
  22. 2023Diffusion Models in Bioinformatics: A New Wave of Deep Learning Revolution in Actioncited by 15
  23. 2023Towards quantitative precision for ECG analysis: Leveraging state space models, self-supervision and patient metadatacited by 15
  24. 2025Unified Uncertainty-Aware Diffusion for Multi-Agent Trajectory Modelingcited by 15
  25. 2025Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradientscited by 15
  26. 2023Diffusion-SS3D: Diffusion Model for Semi-supervised 3D Object Detectioncited by 14
  27. 2024Diffusion-Based Environment-Aware Trajectory Predictioncited by 14
  28. 2025Provable Separations between Memorization and Generalization in Diffusion Modelscited by 14
  29. 2024Latent Diffusion for Neural Spiking Datacited by 12
  30. 2024Generative AI-Driven Human Digital Twin in IoT-Healthcare: A Comprehensive Surveycited by 11
  31. 2024ANT: Adaptive Noise Schedule for Time Series Diffusion Modelscited by 11
  32. 2025Diffusion Models for Time Series Forecasting: A Surveycited by 11
  33. 2023BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decompositioncited by 10
  34. 2024TimeLDM: Latent Diffusion Model for Unconditional Time Series Generationcited by 10
  35. 2025From Samples to Scenarios: A New Paradigm for Probabilistic Forecastingcited by 10
  36. 2022Advancing the State-of-the-Art for ECG Analysis through Structured State Space Modelscited by 9
  37. 2023DiffECG: A Versatile Probabilistic Diffusion Model for ECG Signals Synthesiscited by 9
  38. 2023DDMT: Denoising Diffusion Mask Transformer Models for Multivariate Time Series Anomaly Detectioncited by 9

50 most cited of 195 All 195 (JSON)

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  1. 2024MTSCI: A Conditional Diffusion Model for Multivariate Time Series Consistent Imputation
  2. 2026Analyzing and Improving Diffusion Models for Time-Series Data Imputation: A Proximal Recursion Perspective
  3. 2025S4M: S4 for multivariate time series forecasting with Missing values
  4. 2025Self-attention-based Diffusion Model for Time-series Imputation in Partial Blackout Scenarios
  5. 2025CoSTI: Consistency Models for (a faster) Spatio-Temporal Imputation
  6. 2024TimeAutoDiff: A Unified Framework for Generation, Imputation, Forecasting, and Time-Varying Metadata Conditioning of Heterogeneous Time Series Tabular Data
  7. 2026Impute-EM: Native Mixed-State Diffusion Models for Heterogeneous Data Imputation
  8. 2023PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation