mlsanityData to 7 Oct 2026

Time Series Diffusion in the Frequency Domain

arXiv 2402.05933 ↗First posted 8 Feb 2024cs.LG cs.AIcited by 35

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Fourier analysis has been an instrumental tool in the development of signal processing. This leads us to wonder whether this framework could similarly benefit generative modelling. In this paper, we explore this question through the scope of time series diffusion models. More specifically, we analyze whether representing time series in the frequency domain is a useful inductive bias for score-based diffusion models. By starting from the canonical SDE formulation of diffusion in the time domain, we show that a dual diffusion process occurs in the frequency domain with an important nuance: Brownian motions are replaced by what we call mirrored Brownian motions, characterized by mirror symmetries among their components. Building on this insight, we show how to adapt the denoising score matching approach to implement diffusion models in the frequency domain. This results in frequency diffusion models, which we compare to canonical time diffusion models. Our empirical evaluation on real-world datasets, covering various domains like healthcare and finance, shows that frequency diffusion models better capture the training distribution than time diffusion models. We explain this observation by showing that time series from these datasets tend to be more localized in the frequency domain than in the time domain, which makes them easier to model in the former case. All our observations point towards impactful synergies between Fourier analysis and diffusion models.

Key facts. Cited by 35 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 21 of its 38 references that are in the map. First posted on arXiv 8 Feb 2024.

Builds on

21 of 38 references.

Closest ancestors · 5

Same direction, newest first

  1. 2022Spectral Diffusion Processes28 Sep
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  3. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  5. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 16

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  3. 2019Analyzing and Improving the Image Quality of StyleGANcited by 3,580
  4. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  5. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,419
  6. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  7. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
  8. 2017Real-valued (Medical) Time Series Generation with Recurrent Conditional GANscited by 329
  9. 2018Adversarial Audio Synthesiscited by 222
  10. 2022Continuous diffusion for categorical datacited by 202
  11. 2019MIMIC-Extract: A Data Extraction, Preprocessing, and Representation Pipeline for MIMIC-IIIcited by 121
  12. 2023MatterGen: a generative model for inorganic materials designcited by 98
4 more
  1. 2018ECG Heartbeat Classification: A Deep Transferable Representationcited by 76
  2. 2023Diffusion Models for Time Series Applications: A Surveycited by 72
  3. 2023A Survey on Deep Learning based Time Series Analysis with Frequency Transformationcited by 40
  4. 2023Frequency Domain-based Dataset Distillationcited by 28

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 6; 2025: 14; 2026: 15.

35 papers.

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  1. 2024Foundation Models for Time Series Analysis: A Tutorial and Surveycited by 234
  2. 2024Deep Time Series Models: A Comprehensive Survey and Benchmarkcited by 191
  3. 2024A Survey on Diffusion Models for Time Series and Spatio-Temporal Datacited by 66
  4. 2025A Fourier Space Perspective on Diffusion Modelscited by 48
  5. 2025Spectral Analysis of Diffusion Models with Application to Schedule Designcited by 12
  6. 2025Shaping Inductive Bias in Diffusion Models through Frequency-Based Noise Controlcited by 11
  7. 2025FreCT: Frequency-augmented Convolutional Transformer for Robust Time Series Anomaly Detectioncited by 10
  8. 2025LSCD: Lomb-Scargle Conditioned Diffusion for Time series Imputationcited by 8
  9. 2025Modeling Human Gaze Behavior with Diffusion Models for Unified Scanpath Predictioncited by 7
  10. 2024FLEXtime: Filterbank learning to explain time seriescited by 6
  11. 2024TimeBridge: Better Diffusion Prior Design with Bridge Models for Time Series Generationcited by 5
  12. 2025NeuralRemaster: Phase-Preserving Diffusion for Structure-Aligned Generationcited by 5
23 more
  1. 2024Channel-aware Contrastive Conditional Diffusion for Multivariate Probabilistic Time Series Forecastingcited by 2
  2. 2025Learning What Matters: Steering Diffusion via Spectrally Anisotropic Forward Noisecited by 2
  3. 2025WaveletDiff: Multilevel Wavelet Diffusion For Time Series Generationcited by 2
  4. 2025TSGDiff: Rethinking Synthetic Time Series Generation from a Pure Graph Perspectivecited by 2
  5. 2025DiM-TS: Bridge the Gap between Selective State Space Models and Time Series for Generative Modelingcited by 2
  6. 2025Translation from Wearable PPG to 12-Lead ECGcited by 1
  7. 2026Spectral Regularization for Diffusion Modelscited by 1
  8. 2026Accelerating Frequency Domain Diffusion Models with Error-Feedback Event-Driven Cachingcited by 1
  9. 2026Cyclostationary Phase Conditioning for Medical Time Series Diffusioncited by 1
  10. 2025Frequency-Constrained Learning for Long-Term Forecastingcited by 0
  11. 2025Preserving Spectral Structure and Statistics in Diffusion Modelscited by 0
  12. 2026From Easy to Hard++: Promoting Differentially Private Image Synthesis Through Spatial-Frequency Curriculumcited by 0
  13. 2026Spectral Diffusion Models on the Spherecited by 0
  14. 2026A Decomposable Forward Process in Diffusion Models for Time-Series Forecastingcited by 0
  15. 2026Analyzing and Improving Diffusion Models for Time-Series Data Imputation: A Proximal Recursion Perspectivecited by 0
  16. 2026Parallel Complex Diffusion for Scalable Time Series Generationcited by 0
  17. 2026Deep Time-Series Forecasting in 10 Years: A Surveycited by 0
  18. 2026GenTS: A Comprehensive Benchmark Library for Generative Time Series Modelscited by 0
  19. 2026Low-Pass Flow Matchingcited by 0
  20. 2026HyFAD: Hybrid Time-Frequency Diffusion with Frequency-Aware Embedding for Time Series Imputationcited by 0
  21. 2026DecoVAE: a Lightweight Interpretable Trend-Seasonal VAE Framework for Efficient Probabilistic Time Series Forecastingcited by 0
  22. 2026Time series generation with spectrally aligned latent flow matchingcited by 0
  23. 2026Wavelet Flow Matching for Time Seriescited by 0

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  1. 2024SigDiffusions: Score-Based Diffusion Models for Time Series via Log-Signature Embeddings
  2. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Models
  3. 2026First Learn, Then Memorize: The Spectral Bias of Diffusion Models
  4. 2023Non-Denoising Forward-Time Diffusions
  5. 2025Cross-Domain Conditional Diffusion Models for Time Series Imputation
  6. 2025Generalization through variance: how noise shapes inductive biases in diffusion models
  7. 2022FP-Diffusion: Improving Score-based Diffusion Models by Enforcing the Underlying Score Fokker-Planck Equation
  8. 2023Generative Fractional Diffusion Models