mlsanityData to 14 Oct 2026

RDIT: Residual-based Diffusion Implicit Models for Probabilistic Time Series Forecasting

arXiv 2509.02341 ↗First posted 2 Sep 2025cs.LG cs.AIcited by 4

Not on the map. Why?

Abstract (arXiv)

Probabilistic Time Series Forecasting (PTSF) plays a critical role in domains requiring accurate and uncertainty-aware predictions for decision-making. However, existing methods offer suboptimal distribution modeling and suffer from a mismatch between training and evaluation metrics. Surprisingly, we found that augmenting a strong point estimator with a zero-mean Gaussian, whose standard deviation matches its training error, can yield state-of-the-art performance in PTSF. In this work, we propose RDIT, a plug-and-play framework that combines point estimation and residual-based conditional diffusion with a bidirectional Mamba network. We theoretically prove that the Continuous Ranked Probability Score (CRPS) can be minimized by adjusting to an optimal standard deviation and then derive algorithms to achieve distribution matching. Evaluations on eight multivariate datasets across varied forecasting horizons demonstrate that RDIT achieves lower CRPS, rapid inference, and improved coverage compared to strong baselines.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 31 of its 42 references that are in the map. First posted on arXiv 2 Sep 2025.

Builds on

31 of 42 references.

References · 31

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2020Denoising Diffusion Implicit Modelscited by 9,781
  3. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,926
  4. 2016Gaussian Error Linear Units (GELUs)cited by 3,502
  5. 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,169
  6. 2022A Time Series is Worth 64 Words: Long-term Forecasting with Transformerscited by 2,039
  7. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,979
  8. 2017Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networkscited by 879
  9. 2024Chronos: Learning the Language of Time Seriescited by 759
  10. 2019Conformalized Quantile Regressioncited by 629
  11. 2020Time Series Forecasting With Deep Learning: A Surveycited by 459
  12. 2018Accurate Uncertainties for Deep Learning Using Calibrated Regressioncited by 422
19 more
  1. 2019Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019cited by 273
  2. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 221
  3. 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 198
  4. 2020Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flowscited by 144
  5. 2024Is Mamba Effective for Time Series Forecasting?cited by 114
  6. 2023Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecastingcited by 88
  7. 2023Non-autoregressive Conditional Diffusion Models for Time Series Predictioncited by 78
  8. 2021Time Series Prediction using Deep Learning Methods in Healthcarecited by 74
  9. 2023Diffusion Models for Time Series Applications: A Surveycited by 72
  10. 2025TimeFilter: Patch-Specific Spatial-Temporal Graph Filtration for Time Series Forecastingcited by 64
  11. 2024An Analysis of Linear Time Series Forecasting Modelscited by 41
  12. 2024A Survey of Deep Learning and Foundation Models for Time Series Forecastingcited by 33
  13. 2023TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Seriescited by 26
  14. 2022Conformal Prediction with Temporal Quantile Adjustmentscited by 25
  15. 2024The Rise of Diffusion Models in Time-Series Forecastingcited by 25
  16. 2024Ada-MSHyper: Adaptive Multi-Scale Hypergraph Transformer for Time Series Forecastingcited by 21
  17. 2023Nominality Score Conditioned Time Series Anomaly Detection by Point/Sequential Reconstructioncited by 17
  18. 2024Time Series Analysis for Education: Methods, Applications, and Future Directionscited by 5
  19. 2024MVG-CRPS: A Robust Loss Function for Multivariate Probabilistic Forecastingcited by 5

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Mind the Residual Gap: Probabilistic Downscaling under Real-World Biascited by 0
  2. 2026DynG-Diff: A State-Aware Dynamic Guidance Diffusion Framework for Probabilistic Time Series Forecastingcited by 0
  3. 2026RDDMPI: Residual Denoising Diffusion Model for Probabilistic Multivariate Time Series Imputationcited by 0
  4. 2026DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecastingcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025SimDiff: Simpler Yet Better Diffusion Model for Time Series Point Forecasting
  2. 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting
  3. 2026GARDiff: Graph-Aligned Residual Diffusion for Probabilistic Multivariate Time-Series Forecasting
  4. 2025Non-stationary Diffusion For Probabilistic Time Series Forecasting
  5. 2025Effective Probabilistic Time Series Forecasting with Fourier Adaptive Noise-Separated Diffusion
  6. 2026Two-stage Odd Residual Flows for Mean-Preserving Probabilistic Time Series Forecasting
  7. 2025Collaborative Deterministic-Probabilistic Forecasting for Diverse Spatiotemporal Systems
  8. 2026When Denoising Hurts: Rethinking the Terminal Step of Diffusion Time Series Forecasters -- Extended Version