Diffusion-based Decoupled Deterministic and Uncertain Framework for Probabilistic Multivariate Time Series Forecasting

Diffusion-based denoising models have demonstrated impressive performance in probabilistic forecasting for multivariate time series (MTS). Nonetheless, existing approaches often model the entire data distribution, neglecting the variability in uncertainty across different components of the time series. This paper introduces a Diffusion-based Decoupled Deterministic and Uncertain ($\mathrm{D^3U}$) framework for probabilistic MTS forecasting. The framework integrates non-probabilistic forecasting with conditional diffusion generation, enabling both accurate point predictions and probabilistic forecasting. $\mathrm{D^3U}$ utilizes a point forecasting model to non-probabilistically model high-certainty components in the time series, generating embedded representations that are conditionally injected into a diffusion model. To better model high-uncertainty components, a patch-based denoising network (PatchDN) is designed in the conditional diffusion model. Designed as a plug-and-play framework, $\mathrm{D^3U}$ can be seamlessly integrated into existing point forecasting models to provide probabilistic forecasting capabilities. It can also be applied to other conditional diffusion methods that incorporate point forecasting models. Experiments on six real-world datasets demonstrate that our method achieves over a 20\% improvement in both point and probabilistic forecasting performance in MTS long-term forecasting compared to state-of-the-art (SOTA) probabilistic forecasting methods. Additionally, extensive ablation studies further validate the effectiveness of the $\mathrm{D^3U}$ framework.