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

2025/09/02 by Chih-Yu Lai, Yu Ning, Lai, Chih-Yu +3
Decision Sciences · Engineering · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Forecasting Techniques and Applications #Machine Learning (cs.LG) #Stock Market Forecasting Methods #Traffic Prediction and Management Techniques

paper · pdf · doi:10.48550/arxiv.2509.02341

openalex publication_date 2025/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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Related

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