mlsanityData to 7 Oct 2026

Wavelet Flow Matching for Time Series

arXiv 2609.39374 ↗First posted 30 Sep 2026cs.LG cs.AIcited by 0

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

Abstract (arXiv)

Synthetic time series are increasingly used for data augmentation, privacy-preserving data sharing, and downstream model development, yet faithfully reproducing both multi-scale temporal structure and cross-channel dependencies remains challenging. We study multivariate time-series generation through flow matching in the wavelet domain. By operating on multilevel discrete wavelet coefficients rather than directly in the time domain, the model represents coarse structure and progressively finer details at separate scales. Their naturally different variances further induce an implicit coarse-to-fine generative process without requiring an explicit multi-scale schedule. Since the transform acts independently on each channel, we pair it with a channel-token transformer whose attention directly models cross-channel dependencies. Across seven benchmark datasets and four sequence lengths, our method is best or tied on a majority of dataset-metric combinations, with the largest and most consistent improvements in Context-FID and discriminative score.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 48 of its 77 references that are in the map. First posted on arXiv 30 Sep 2026.

Builds on

48 of 77 references.

Closest ancestors · 8

Same direction, newest first

  1. 2024FlowTS: Time Series Generation via Rectified Flow12 Nov
  2. 2024Utilizing Image Transforms and Diffusion Models for Generative Modeling of Short and Long Time Series25 Oct
  3. 2024Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting3 Oct
  4. 2024Diffusion-TS: Interpretable Diffusion for General Time Series Generation4 Mar
  5. 2023Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting21 Jul
  6. 2022Flow Matching for Generative Modeling6 Oct
  7. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep
  8. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation7 Jul

Other references · 40

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  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  5. 2022Scalable Diffusion Models with Transformerscited by 5,931
  6. 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesiscited by 4,094
  7. 2014Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translationcited by 4,016
  8. 2018Neural Ordinary Differential Equationscited by 3,733
  9. 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,141
  10. 2022A Time Series is Worth 64 Words: Long-term Forecasting with Transformerscited by 1,981
  11. 2021Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecastingcited by 1,654
  12. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
28 more
  1. 2023iTransformer: Inverted Transformers Are Effective for Time Series Forecastingcited by 906
  2. 2017Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networkscited by 869
  3. 2021TS2Vec: Towards Universal Representation of Time Seriescited by 463
  4. 2017Real-valued (Medical) Time Series Generation with Recurrent Conditional GANscited by 329
  5. 2022Perception Prioritized Training of Diffusion Modelscited by 301
  6. 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 195
  7. 2021TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generationcited by 139
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  9. 2022Wavelet Diffusion Models are fast and scalable Image Generatorscited by 116
  10. 2018Multilevel Wavelet Decomposition Network for Interpretable Time Series Analysiscited by 61
  11. 2022Wavelet Score-Based Generative Modelingcited by 61
  12. 2021PSA-GAN: Progressive Self Attention GANs for Synthetic Time Seriescited by 58
  13. 2023Vector Quantized Time Series Generation with a Bidirectional Prior Modelcited by 49
  14. 2023Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEscited by 48
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  16. 2022GT-GAN: General Purpose Time Series Synthesis with Generative Adversarial Networkscited by 43
  17. 2024Time Series Diffusion in the Frequency Domaincited by 35
  18. 2022Progressive Deblurring of Diffusion Models for Coarse-to-Fine Image Synthesiscited by 34
  19. 2021Adaptive wavelet distillation from neural networks through interpretationscited by 32
  20. 2021Fully Learnable Deep Wavelet Transform for Unsupervised Monitoring of High-Frequency Time Seriescited by 29
  21. 2020Conditional Sig-Wasserstein GANs for Time Series Generationcited by 23
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  23. 2024AdaWaveNet: Adaptive Wavelet Network for Time Series Analysiscited by 5
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  25. 2024TreeDiffusion: Hierarchical Generative Clustering for Conditional Diffusioncited by 2
  26. 2025WaveletDiff: Multilevel Wavelet Diffusion For Time Series Generationcited by 2
  27. 2026Functional MRI Time Series Generation via Wavelet-Based Image Transform and Spectral Flow Matching for Brain Disorder Identificationcited by 2
  28. 2026Cyclostationary Phase Conditioning for Medical Time Series Diffusioncited by 1

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  6. 2025Time Series Generation Under Data Scarcity: A Unified Generative Modeling Approach
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