mlsanityData to 14 Oct 2026

Non-stationary Diffusion For Probabilistic Time Series Forecasting

arXiv 2505.04278 ↗First posted 7 May 2025cs.LG cs.AIcited by 27

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

Abstract (arXiv)

Due to the dynamics of underlying physics and external influences, the uncertainty of time series often varies over time. However, existing Denoising Diffusion Probabilistic Models (DDPMs) often fail to capture this non-stationary nature, constrained by their constant variance assumption from the additive noise model (ANM). In this paper, we innovatively utilize the Location-Scale Noise Model (LSNM) to relax the fixed uncertainty assumption of ANM. A diffusion-based probabilistic forecasting framework, termed Non-stationary Diffusion (NsDiff), is designed based on LSNM that is capable of modeling the changing pattern of uncertainty. Specifically, NsDiff combines a denoising diffusion-based conditional generative model with a pre-trained conditional mean and variance estimator, enabling adaptive endpoint distribution modeling. Furthermore, we propose an uncertainty-aware noise schedule, which dynamically adjusts the noise levels to accurately reflect the data uncertainty at each step and integrates the time-varying variances into the diffusion process. Extensive experiments conducted on nine real-world and synthetic datasets demonstrate the superior performance of NsDiff compared to existing approaches. Code is available at https://github.com/wwy155/NsDiff.

Key facts. Cited by 27 papers in the map (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 29 of its 46 references that are in the map. First posted on arXiv 7 May 2025.

Builds on

29 of 46 references.

Closest ancestors · 5

Same direction, newest first

  1. 2024ANT: Adaptive Noise Schedule for Time Series Diffusion Models18 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. 2023Non-autoregressive Conditional Diffusion Models for Time Series Prediction8 Jun
  5. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation7 Jul

Other references · 24

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  3. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,352
  4. 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,169
  5. 2022A Time Series is Worth 64 Words: Long-term Forecasting with Transformerscited by 2,039
  6. 2022Are Transformers Effective for Time Series Forecasting?cited by 1,424
  7. 2022TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysiscited by 1,058
  8. 2017Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networkscited by 879
  9. 2021Vector Quantized Diffusion Model for Text-to-Image Synthesiscited by 774
  10. 2020Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networkscited by 566
  11. 2022Non-stationary Transformers: Exploring the Stationarity in Time Series Forecastingcited by 391
  12. 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 198
12 more
  1. 2021AdaRNN: Adaptive Learning and Forecasting of Time Seriescited by 121
  2. 2023Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictorscited by 113
  3. 2023Dish-TS: A General Paradigm for Alleviating Distribution Shift in Time Series Forecastingcited by 93
  4. 2023Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglementcited by 90
  5. 2024Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processescited by 66
  6. 2024Frequency Adaptive Normalization For Non-stationary Time Series Forecastingcited by 47
  7. 2023Training neural operators to preserve invariant measures of chaotic attractorscited by 46
  8. 2022Koopman Neural Forecaster for Time Series with Temporal Distribution Shiftscited by 37
  9. 2022DDG-DA: Data Distribution Generation for Predictable Concept Drift Adaptationcited by 36
  10. 2023Provably Convergent Schr"odinger Bridge with Applications to Probabilistic Time Series Imputationcited by 27
  11. 2024Deep Frequency Derivative Learning for Non-stationary Time Series Forecastingcited by 13
  12. 2024Ordering-Based Causal Discovery for Linear and Nonlinear Relationscited by 13

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 4; 2026: 23.

27 papers.

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  1. 2026AutoSOTA: An End-to-End Automated Research System for State-of-the-Art AI Model Discoverycited by 23
  2. 2025Diffusion Models for Time Series Forecasting: A Surveycited by 11
  3. 2025From Samples to Scenarios: A New Paradigm for Probabilistic Forecastingcited by 10
  4. 2025EventTSF: Event-Aware Non-Stationary Time Series Forecastingcited by 2
  5. 2026StaTS: Spectral Trajectory Schedule Learning for Adaptive Time Series Forecasting with Frequency Guided Denoisercited by 1
  6. 2026ZeroDiff: Zero-Shot Time Series Reconstruction via Informed-Prior Diffusioncited by 1
  7. 2025Conditionally Whitened Generative Models for Probabilistic Time Series Forecastingcited by 0
  8. 2026CoGenCast: A Coupled Autoregressive-Flow Generative Framework for Time Series Forecastingcited by 0
  9. 2026DECODE: Dual-Enhanced Conditioned Diffusion for EEG Forecastingcited by 0
  10. 2026Deep Time-Series Forecasting in 10 Years: A Surveycited by 0
  11. 2026Beyond Static Uncertainty: Modeling Temporal Uncertainty Dynamics for Probabilistic Time Series Forecastingcited by 0
  12. 2026SURGE: An Event-Centric Social Media Sentiment Time Series Benchmark with Interaction Structurecited by 0
15 more
  1. 2026Parametric Prior Mapping Framework for Non-stationary Probabilistic Time Series Forecastingcited by 0
  2. 2026ProbRes: Volatility Learning for Probabilistic Time-Series Forecastingcited by 0
  3. 2026StrideDiffusion: Accelerating Diffusion Models for Time-series Generationcited by 0
  4. 2026Differencing the Diffusion Trajectory toward Uncertain Components for Time Series Forecastingcited by 0
  5. 2026Evaluating Generative Time-Series Models on Data with Point Massescited by 0
  6. 2026SCENARIODIFF: A Scenario-level Guidance Framework for Multimodal Time Series Forecasting--Extended Versioncited by 0
  7. 2026SPACE: Sample-cloud Predictive Adaptive Conformal Ellipsoids for Multivariate Time-Series Forecastingcited by 0
  8. 2026DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecastingcited by 0
  9. 2026TimeES: Probabilistic and Deterministic Time Series Forecasting via Evolutionary Spectracited by 0
  10. 2026KiT: A Foundation Model for Financial Time-Series Forecasting using DiffusionTransformerscited by 0
  11. 2026Retrieval-Augmented Diffusion Modeling for Stochastic Discount Factor Portfolioscited by 0
  12. 2026GARDiff: Graph-Aligned Residual Diffusion for Probabilistic Multivariate Time-Series Forecastingcited by 0
  13. 2026ProtoFlow: Prototype-Guided Flow Matching for Multivariate Time Series Forecastingcited by 0
  14. 2026NV-Tesseract-AD: Curriculum-Enhanced Conditional Diffusion for Multivariate Time-Series Anomaly Detectioncited by 0
  15. 2026Deterministic Prediction as Global Velocity: Flow Matching for Probabilistic Time-Series Forecastcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting
  2. 2025Effective Probabilistic Time Series Forecasting with Fourier Adaptive Noise-Separated Diffusion
  3. 2024Conditional Denoising Meets Polynomial Modeling: A Flexible Decoupled Framework for Time Series Forecasting
  4. 2026When Denoising Hurts: Rethinking the Terminal Step of Diffusion Time Series Forecasters -- Extended Version
  5. 2024Channel-aware Contrastive Conditional Diffusion for Multivariate Probabilistic Time Series Forecasting
  6. 2023Add and Thin: Diffusion for Temporal Point Processes
  7. 2025SimDiff: Simpler Yet Better Diffusion Model for Time Series Point Forecasting
  8. 2026DynG-Diff: A State-Aware Dynamic Guidance Diffusion Framework for Probabilistic Time Series Forecasting