SSD-TS: Exploring the Potential of Linear State Space Models for Diffusion Models in Time Series Imputation

Probabilistic time series imputation has been widely applied in real-world scenarios due to its ability for uncertainty estimation and denoising diffusion probabilistic models~(DDPMs) have achieved great success in probabilistic time series imputation tasks with its power to model complex distributions. However, current DDPM-based probabilistic time series imputation methodologies are confronted with two types of challenges: 1)$\mathit{\text{The}}\mathit{\text{backbone}}\mathit{\text{modules}}\mathit{\text{of}}\mathit{\text{the}}\mathit{\text{denoising}}\mathit{\text{parts}}\mathit{\text{are}}\mathit{\text{not}}\mathit{\text{capable}}\mathit{\text{of}}\mathit{\text{achieving}}\mathit{\text{sequence}}\mathit{\text{modeling}}\mathit{\text{with}}\mathit{\text{low}}\mathit{\text{time}}\mathit{\text{complexity.}}$ 2)~$\mathit{\text{The}}\mathit{\text{architecture}}\mathit{\text{of}}\mathit{\text{denoising}}\mathit{\text{modules}}\mathit{\text{can}}\mathit{\text{not}}\mathit{\text{handle}}\mathit{\text{the}}\mathit{\text{dependencies}}\mathit{\text{in}}\mathit{\text{the}}\mathit{\text{time}}\mathit{\text{series}}\mathit{\text{data}}\mathit{\text{effectively.}}$ To address the first challenge, we explore the potential of state space model, namely Mamba, as the backbone denoising module for DDPMs. To tackle the second challenge, we carefully devise several SSM-based blocks for time series data modeling. Experimental results demonstrate that our approach can achieve state-of-the-art time series imputation results on multiple real-world datasets. Our datasets and code are available at \href{https://github.com/decisionintelligence/SSD-TS/}{https://github.com/decisionintelligence/SSD-TS/}