mlsanityData to 7 Oct 2026

HyFAD: Hybrid Time-Frequency Diffusion with Frequency-Aware Embedding for Time Series Imputation

arXiv 2606.05239 ↗First posted 3 Jun 2026stat.ML cs.LGcited by 0

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

Abstract (arXiv)

Diffusion models have demonstrated strong performance in time series modeling due to their ability to progressively capture complex data distributions through iterative denoising. However, existing approaches struggle with frequency-sensitive denoising, high-frequency reconstruction and balancing global trends with local dynamics. To address these limitations, we propose HyFAD, a Hybrid time-frequency Diffusion model with Frequency-Aware embedding for time series imputation. Built upon the DDPM paradigm, HyFAD adopts a coupled time-frequency diffusion framework, in which the reverse denoising proceeds sequentially from the time domain to the frequency domain, enabling coarse-to-fine generation. Specifically, the time-domain diffusion process captures low-frequency global trends, while the frequency-domain diffusion process refines high-frequency spectral components. We further introduce a frequency-aware step embedding that exploits the relationship between diffusion steps and spectral components, providing step-dependent spectral guidance and facilitates more accurate band-wise reconstruction. Extensive experiments on multiple benchmark datasets demonstrate that HyFAD achieves state-of-the-art performance. Our source code is available at https://github.com/hongfangao/HyFAD.

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 28 of its 40 references that are in the map. First posted on arXiv 3 Jun 2026.

Builds on

28 of 40 references.

Closest ancestors · 5

Same direction, newest first

  1. 2024Utilizing Image Transforms and Diffusion Models for Generative Modeling of Short and Long Time Series25 Oct
  2. 2024Diffusion-TS: Interpretable Diffusion for General Time Series Generation4 Mar
  3. 2023Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting21 Jul
  4. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation7 Jul
  5. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting28 Jan

Other references · 23

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2020Denoising Diffusion Implicit Modelscited by 9,655
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  6. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  7. 2022Scalable Diffusion Models with Transformerscited by 5,931
  8. 2022FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecastingcited by 1,200
  9. 2022TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysiscited by 1,030
  10. 2018BRITS: Bidirectional Recurrent Imputation for Time Seriescited by 288
  11. 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 195
  12. 2019GP-VAE: Deep Probabilistic Time Series Imputationcited by 171
11 more
  1. 2022SAITS: Self-Attention-based Imputation for Time Seriescited by 167
  2. 2022FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecastingcited by 147
  3. 2022Diffusion Probabilistic Model Made Slimcited by 121
  4. 2024Boosting Diffusion Models with Moving Average Sampling in Frequency Domaincited by 53
  5. 2023On the Constrained Time-Series Generation Problemcited by 52
  6. 2022TFAD: A Decomposition Time Series Anomaly Detection Architecture with Time-Frequency Analysiscited by 48
  7. 2025A Fourier Space Perspective on Diffusion Modelscited by 48
  8. 2021ScoreGrad: Multivariate Probabilistic Time Series Forecasting with Continuous Energy-based Generative Modelscited by 42
  9. 2024Time Series Diffusion in the Frequency Domaincited by 35
  10. 2024DCTdiff: Intriguing Properties of Image Generative Modeling in the DCT Spacecited by 32
  11. 2025LSCD: Lomb-Scargle Conditioned Diffusion for Time series Imputationcited by 8

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  1. 2025Cross-Domain Conditional Diffusion Models for Time Series Imputation
  2. 2026Analyzing and Improving Diffusion Models for Time-Series Data Imputation: A Proximal Recursion Perspective
  3. 2026Discretizing Continuous Time Series for Imputation with Masked Diffusion Training
  4. 2026RDDMPI: Residual Denoising Diffusion Model for Probabilistic Multivariate Time Series Imputation
  5. 2026Accelerating Frequency Domain Diffusion Models with Error-Feedback Event-Driven Caching
  6. 2024MTSCI: A Conditional Diffusion Model for Multivariate Time Series Consistent Imputation
  7. 2025Diffusion Transformers for Imputation: Statistical Efficiency and Uncertainty Quantification
  8. 2026Parallel Complex Diffusion for Scalable Time Series Generation