Conditional Denoising Meets Polynomial Modeling: A Flexible Decoupled Framework for Time Series Forecasting

Abstract

Time series forecasting models are becoming increasingly prevalent due to their critical role in decision-making across various domains. However, most existing approaches represent the coupled temporal patterns, often neglecting the distinction between their specific components. In particular, fluctuating patterns and smooth trends within time series exhibit distinct characteristics. In this work, to model complicated temporal patterns, we propose a Conditional Denoising Polynomial Modeling (CDPM) framework, where probabilistic diffusion models and deterministic linear models are trained end-to-end. Instead of modeling the coupled time series, CDPM decomposes it into trend and seasonal components for modeling them separately. To capture the fluctuating seasonal component, we employ a probabilistic diffusion model based on statistical properties from the historical window. For the smooth trend component, a module is proposed to enhance linear models by incorporating historical dependencies, thereby preserving underlying trends and mitigating noise distortion. Extensive experiments conducted on six benchmarks demonstrate the effectiveness of our framework, highlighting the potential of combining probabilistic and deterministic models. Our code is available at https://github.com/zjt-gpu/CDPM.