mlsanityData to 7 Oct 2026

A Decomposable Forward Process in Diffusion Models for Time-Series Forecasting

arXiv 2601.21812 ↗First posted 29 Jan 2026stat.ML cs.AI cs.LGcited by 0

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

Abstract (arXiv)

We introduce a model-agnostic forward diffusion process for time-series forecasting that decomposes signals into spectral components, preserving structured temporal patterns such as seasonality more effectively than standard diffusion. Unlike prior work that modifies the network architecture or diffuses directly in the frequency domain, our proposed method alters only the diffusion process itself, making it compatible with existing diffusion backbones (e.g., DiffWave, TimeGrad, CSDI). By staging noise injection according to component energy, it maintains high signal-to-noise ratios for dominant frequencies throughout the diffusion trajectory, thereby improving the recoverability of long-term patterns. This strategy enables the model to maintain the signal structure for a longer period in the forward process, leading to improved forecast quality. Across standard forecasting benchmarks, we show that applying spectral decomposition strategies, such as the Fourier or Wavelet transform, consistently improves upon diffusion models using the baseline forward process, with negligible computational overhead. The code for this paper is available at https://anonymous.4open.science/r/D-FDP-4A29.

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 38 of its 63 references that are in the map. First posted on arXiv 29 Jan 2026.

Builds on

38 of 63 references.

Closest ancestors · 4

Same direction, newest first

  1. 2024MG-TSD: Multi-Granularity Time Series Diffusion Models with Guided Learning Process9 Mar
  2. 2024Diffusion-TS: Interpretable Diffusion for General Time Series Generation4 Mar
  3. 2023Non-autoregressive Conditional Diffusion Models for Time Series Prediction8 Jun
  4. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation7 Jul

Other references · 34

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2020Denoising Diffusion Implicit Modelscited by 9,655
  4. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  6. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  7. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  8. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,424
  9. 2022Video Diffusion Modelscited by 2,280
  10. 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,141
  11. 2016WaveNet: A Generative Model for Raw Audiocited by 1,710
  12. 2022Are Transformers Effective for Time Series Forecasting?cited by 1,400
22 more
  1. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  2. 2022FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecastingcited by 1,200
  3. 2021Cascaded Diffusion Models for High Fidelity Image Generationcited by 1,155
  4. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  5. 2022TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysiscited by 1,030
  6. 2019N-BEATS: Neural basis expansion analysis for interpretable time series forecastingcited by 744
  7. 2021Diffusion Probabilistic Models for 3D Point Cloud Generationcited by 734
  8. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 620
  9. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  10. 2020Time Series Forecasting With Deep Learning: A Surveycited by 457
  11. 2022Understanding Diffusion Models: A Unified Perspectivecited by 337
  12. 2023NaturalSpeech 2: Latent Diffusion Models are Natural and Zero-Shot Speech and Singing Synthesizerscited by 233
  13. 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 195
  14. 2019Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directionscited by 172
  15. 2022It's Raw! Audio Generation with State-Space Modelscited by 171
  16. 2023Frequency-domain MLPs are More Effective Learners in Time Series Forecastingcited by 170
  17. 2021Learning to Efficiently Sample from Diffusion Probabilistic Modelscited by 129
  18. 2024TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysiscited by 113
  19. 2024CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patternscited by 102
  20. 2021ScoreGrad: Multivariate Probabilistic Time Series Forecasting with Continuous Energy-based Generative Modelscited by 42
  21. 2024Time Series Diffusion in the Frequency Domaincited by 35
  22. 2021NRTSI: Non-Recurrent Time Series Imputationcited by 25

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  5. 2026StaTS: Spectral Trajectory Schedule Learning for Adaptive Time Series Forecasting with Frequency Guided Denoiser
  6. 2025WaveletDiff: Multilevel Wavelet Diffusion For Time Series Generation
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