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

arXiv: https://arxiv.org/abs/2509.02341 · HTML: https://mlsanity.com/paper/2509.02341/

## 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 (most cited first, 30 of 31)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Is Mamba Effective for Time Series Forecasting?](https://mlsanity.com/paper/2403.11144/) (2024)
- [Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2307.11494/) (2023)
- [Non-autoregressive Conditional Diffusion Models for Time Series Prediction](https://mlsanity.com/paper/2306.05043/) (2023)
- [Time Series Prediction using Deep Learning Methods in Healthcare](https://mlsanity.com/paper/2108.13461/) (2021)
- [Diffusion Models for Time Series Applications: A Survey](https://mlsanity.com/paper/2305.00624/) (2023)
- [TimeFilter: Patch-Specific Spatial-Temporal Graph Filtration for Time Series Forecasting](https://mlsanity.com/paper/2501.13041/) (2025)
- [An Analysis of Linear Time Series Forecasting Models](https://mlsanity.com/paper/2403.14587/) (2024)
- [A Survey of Deep Learning and Foundation Models for Time Series Forecasting](https://mlsanity.com/paper/2401.13912/) (2024)
- [TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Series](https://mlsanity.com/paper/2310.01327/) (2023)
- [Conformal Prediction with Temporal Quantile Adjustments](https://mlsanity.com/paper/2205.09940/) (2022)
- [The Rise of Diffusion Models in Time-Series Forecasting](https://mlsanity.com/paper/2401.03006/) (2024)
- [Ada-MSHyper: Adaptive Multi-Scale Hypergraph Transformer for Time Series Forecasting](https://mlsanity.com/paper/2410.23992/) (2024)
- [Nominality Score Conditioned Time Series Anomaly Detection by Point/Sequential Reconstruction](https://mlsanity.com/paper/2310.15416/) (2023)
- [Time Series Analysis for Education: Methods, Applications, and Future Directions](https://mlsanity.com/paper/2408.13960/) (2024)

## Built on by (most cited first, 4 of 4)

- [Mind the Residual Gap: Probabilistic Downscaling under Real-World Bias](https://mlsanity.com/paper/2606.30821/) (2026)
- [DynG-Diff: A State-Aware Dynamic Guidance Diffusion Framework for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2609.02068/) (2026)
- [RDDMPI: Residual Denoising Diffusion Model for Probabilistic Multivariate Time Series Imputation](https://mlsanity.com/paper/2609.11648/) (2026)
- [DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2609.32363/) (2026)

## 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.