Breaking the Limits of Autoregression! A Diffusion-Bridge with Mutual-Information for Time Series Forecasting

Jiacheng Li, Wei Chen, Junmei Yang, Zhiheng Zhou, Delu Zeng

Keywords: Time series forecasting; Autoregression; Diffusion; Mutual-Information

TL;DR: A new time series forecasting method Auto-Regressive Diffusion Bridge with Mutual-Information correction

Abstract: Time series forecasting (TSF) is a fundamental task in many real-world applications, yet effectively modeling both global dependencies and local dynamics remains challenging. Existing diffusion-based approaches typically adopt a noise-driven paradigm, which disrupts temporal continuity and fails to leverage intermediate evolutionary states, thereby limiting forecasting accuracy and robustness. To overcome these limitations, we propose \textbf{AR-DBMI} (\textbf{A}uto-\textbf{R}egressive \textbf{D}iffusion \textbf{B}ridge with \textbf{M}utual-\textbf{I}nformation correction), a novel generative forecasting framework. AR-DBMI reformulates time series evolution as a ``future-to-history'' diffusion bridge, where intermediate states are deterministically generated through sliding operations to preserve transitional dynamics. To further enhance performance, we introduce a velocity-consistency constraint to capture first-order dynamics across windows, and a mutual-information alignment mechanism to ensure semantic consistency between predicted and ground-truth endpoints. In addition, dual-domain regularization combining time-domain anchoring and spectral consistency improves stability under non-stationary and noisy conditions. Extensive experiments conducted on seven widely used datasets demonstrate that our model achieves state-of-the-art performance, significantly outperforming existing diffusion-based TSF models.

Primary Area: learning on time series and dynamical systems

Submission Number: 4438