Dynamic Decomposition Diffusion Model for Probabilistic Multivariate Time Series Forecasting

Abstract

Accurate probabilistic forecasting of multivariate time series (MTS) is crucial for many real-world applications but remains challenging due to the inherent complexity and non-stationarity of these signals. To address these challenges, we propose the Dynamic Decomposition Diffusion Model (D3M), which integrates advanced signal decomposition techniques with diffusion-based generative models. D3M dynamically decomposes MTS into narrowband intrinsic mode functions (IMFs) and employs a patching channel-independence transformer to efficiently manage the increased data dimensionality. A conditional diffusion model estimates the probabilistic distributions of the decomposed components, with the final MTS distribution obtained as the joint distribution of all components. These modules are seamlessly unified within a Bayesian joint optimization framework, improving forecasting accuracy and uncertainty quantification. Experimental results on six real-world datasets confirm that D3M consistently outperforms state-of-the-art methods in both accuracy and robustness.