Title: Conditional Guided Flow Matching: Modeling Prediction Residuals for Enhanced Time Series Forecasting
Primary area: learning on time series and dynamical systems
Keywords: Time Serires Forecasting, Flow Matching, Generative modeling, Deep Learning

Abstract: Time series forecasting predominantly focuses on modeling the mapping between historical and future sequences, and existing improvements are often constrained to optimizing model architectures to better capture this relationship. This essentially reduces prediction residuals to mere optimization targets while overlooking their informative structures such as systematic biases or nontrivial distributions that could otherwise be exploited to directly reduce forecasting errors. Unfortunately, discriminative models struggle to capture the complete residual structure and its dynamic temporal dependencies when applied to residual learning. To fill this gap, we introduce Conditional Guided Flow Matching (CGFM), a novel framework built upon flow matching. CGFM innovatively leverages auxiliary predictions as the source distribution and constructs two-sided conditional paths to prevent path crossing, which enables the explicit learning of the full structure of prediction residuals and thereby theoretically guarantees superior performance over discriminative models. Extensive experiments show that CGFM enhances diverse forecasting models including
state-of-the-art ones and demonstrates its effectiveness and generality. Code link: \url{https://anonymous.4open.science/r/CGFM-31DB}.