mlsanityData to 7 Oct 2026

Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusion

arXiv 2211.02590 ↗First posted 4 Nov 2022cs.LGcited by 39

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Abstract (arXiv)

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). Builds on 37 of its 57 references that are in the map. First posted on arXiv 4 Nov 2022.

Builds on

37 of 57 references.

References · 37

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  7. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  8. 2022Generative Adversarial Networkscited by 5,603
  9. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  10. 2018Neural Ordinary Differential Equationscited by 3,733
  11. 2014Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modelingcited by 2,341
  12. 2016Density estimation using Real NVPcited by 2,029
25 more
  1. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  2. 2017Deep Setscited by 1,394
  3. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  4. 2021Variational Diffusion Modelscited by 1,145
  5. 2017DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networkscited by 1,004
  6. 2020Meta-Learning in Neural Networks: A Surveycited by 944
  7. 2017Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networkscited by 869
  8. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 577
  9. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecastingcited by 332
  10. 2018Neural Processescited by 307
  11. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contractioncited by 306
  12. 2019Attentive Neural Processescited by 280
  13. 2020Scalable Gradients for Stochastic Differential Equationscited by 264
  14. 2021Gotta Go Fast When Generating Data with Score-Based Modelscited by 218
  15. 2021Neural SDEs as Infinite-Dimensional GANscited by 159
  16. 2019High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processescited by 147
  17. 2020Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flowscited by 142
  18. 2022Accelerating Diffusion Models via Early Stop of the Diffusion Processcited by 100
  19. 2022Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Modelscited by 97
  20. 2022Neural Diffusion Processescited by 50
  21. 2020Modeling Continuous Stochastic Processes with Dynamic Normalizing Flowscited by 37
  22. 2022Spectral Diffusion Processescited by 24
  23. 2020If You Like It, GAN It. Probabilistic Multivariate Times Series Forecast With GANcited by 14
  24. 2021Continuous Latent Process Flowscited by 10
  25. 2022Random Noise vs State-of-the-Art Probabilistic Forecasting Methods : A Case Study on CRPS-Sum Discrimination Abilitycited by 7

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 6; 2024: 15; 2025: 12; 2026: 6.

39 papers.

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  1. 2024Time-MMD: Multi-Domain Multimodal Dataset for Time Series Analysiscited by 65
  2. 2024Deep Learning for Multivariate Time Series Imputation: A Surveycited by 57
  3. 2024Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecastingcited by 40
  4. 2023ProbTS: Benchmarking Point and Distributional Forecasting across Diverse Prediction Horizonscited by 35
  5. 2024Universal Time-Series Representation Learning: A Surveycited by 28
  6. 2023TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Seriescited by 25
  7. 2024The Rise of Diffusion Models in Time-Series Forecastingcited by 25
  8. 2023Reliable Generation of Privacy-preserving Synthetic Electronic Health Record Time Series via Diffusion Modelscited by 24
  9. 2023Add and Thin: Diffusion for Temporal Point Processescited by 22
  10. 2023Time Series Continuous Modeling for Imputation and Forecasting with Implicit Neural Representationscited by 16
  11. 2024Stochastic Optimal Control for Diffusion Bridges in Function Spacescited by 16
  12. 2025Generating Full-field Evolution of Physical Dynamics from Irregular Sparse Observationscited by 8
27 more
  1. 2025LSCD: Lomb-Scargle Conditioned Diffusion for Time series Imputationcited by 8
  2. 2025From Samples to Scenarios: A New Paradigm for Probabilistic Forecastingcited by 8
  3. 2025In-Context Learning of Stochastic Differential Equations with Foundation Inference Modelscited by 7
  4. 2024Constrained Posterior Sampling: Time Series Generation with Hard Constraintscited by 6
  5. 2025Koopman-Equivariant Gaussian Processescited by 6
  6. 2024How Deep is your Guess? A Fresh Perspective on Deep Learning for Medical Time-Series Imputationcited by 5
  7. 2024TimeBridge: Better Diffusion Prior Design with Bridge Models for Time Series Generationcited by 5
  8. 2025TRADES: Generating Realistic Market Simulations with Diffusion Modelscited by 5
  9. 2024TimeAutoDiff: A Unified Framework for Generation, Imputation, Forecasting, and Time-Varying Metadata Conditioning of Heterogeneous Time Series Tabular Datacited by 4
  10. 20243D Object Detection from Point Cloud via Voting Step Diffusioncited by 3
  11. 2024Conditional Lagrangian Wasserstein Flow for Time Series Imputationcited by 3
  12. 2024Conditional Denoising Meets Polynomial Modeling: A Flexible Decoupled Framework for Time Series Forecastingcited by 3
  13. 2025FNOPE: Simulation-based inference on function spaces with Fourier Neural Operatorscited by 3
  14. 2024Channel-aware Contrastive Conditional Diffusion for Multivariate Probabilistic Time Series Forecastingcited by 2
  15. 2025Generative Unordered Flow for Set-Structured Data Generationcited by 2
  16. 2025A Jump-Diffusion Framework for Irregular Time Series Generationcited by 2
  17. 2026Is Flow Matching Just Trajectory Replay for Sequential Data?cited by 2
  18. 2023Predicting the Position Uncertainty at the Time of Closest Approach with Diffusion Modelscited by 1
  19. 2025MoTM: Towards a Foundation Model for Time Series Imputation based on Continuous Modelingcited by 1
  20. 2024ProGen: Revisiting Probabilistic Spatial-Temporal Time Series Forecasting from a Continuous Generative Perspective Using Stochastic Differential Equationscited by 0
  21. 2025Towards High Resolution Probabilistic Coastal Inundation Forecasting from Sparse Observationscited by 0
  22. 2025Conditionally Whitened Generative Models for Probabilistic Time Series Forecastingcited by 0
  23. 2026Unconditional flow-based time series generation with equivariance-regularised latent spacescited by 0
  24. 2026Prior-Fitted Functional Flow: In-Context Generative Models for Pharmacokineticscited by 0
  25. 2026Universal Time Series Generation with Neural Controlled Differential Equationscited by 0
  26. 2026SynEnergy: Anomaly Semantic-Guided Diffusion for Synthetic Energy Data Generationcited by 0
  27. 2026Time series generation with spectrally aligned latent flow matchingcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025TIMED: Adversarial and Autoregressive Refinement of Diffusion-Based Time Series Generation
  2. 2023To smooth a cloud or to pin it down: Guarantees and Insights on Score Matching in Denoising Diffusion Models
  3. 2024Discrete vs. Continuous Trade-offs for Generative Models
  4. 2023Score-based Diffusion Models in Function Space
  5. 2023Diffusion Models for Time Series Applications: A Survey
  6. 2026A Decomposable Forward Process in Diffusion Models for Time-Series Forecasting
  7. 2022From Denoising Diffusions to Denoising Markov Models
  8. 2023Non-Autoregressive Diffusion-based Temporal Point Processes for Continuous-Time Long-Term Event Prediction