DiM-TS: Bridge the Gap between Selective State Space Models and Time Series for Generative Modeling

TL;DR

DiM-TS presents a diffusion-based framework that bridges selective State Space Models with time-series generation. By introducing Lag Fusion Mamba for temporal denoising and Permutation Scanning Mamba for channel denoising, it unifies with the original Mamba under a matrix multiplication view, enabling explicit modeling of periodicity and inter-channel dependencies. Through a dual-branch encoder-decoder architecture and multi-feature losses, DiM-TS achieves superior fidelity across multiple public datasets and maintains performance on longer sequences. The approach offers a principled, scalable path for privacy-preserving, high-quality time-series synthesis with strong practical implications for downstream forecasting and analysis.

Abstract

Time series data plays a pivotal role in a wide variety of fields but faces challenges related to privacy concerns. Recently, synthesizing data via diffusion models is viewed as a promising solution. However, existing methods still struggle to capture long-range temporal dependencies and complex channel interrelations. In this research, we aim to utilize the sequence modeling capability of a State Space Model called Mamba to extend its applicability to time series data generation. We firstly analyze the core limitations in State Space Model, namely the lack of consideration for correlated temporal lag and channel permutation. Building upon the insight, we propose Lag Fusion Mamba and Permutation Scanning Mamba, which enhance the model's ability to discern significant patterns during the denoising process. Theoretical analysis reveals that both variants exhibit a unified matrix multiplication framework with the original Mamba, offering a deeper understanding of our method. Finally, we integrate two variants and introduce Diffusion Mamba for Time Series (DiM-TS), a high-quality time series generation model that better preserves the temporal periodicity and inter-channel correlations. Comprehensive experiments on public datasets demonstrate the superiority of DiM-TS in generating realistic time series while preserving diverse properties of data.

Figures (13)

• Figure 1: Comparison of ACF values, the latent state in original SSMs, and the lag fused state. We reshape them into a 2D format for clearer presentation. While the original latent state fails to capture periodic dependencies observed in ACF values, the lag fused state performs better in this regard.
• Figure 2: Proposed DiM-TS framework. Diffusion State Fusion Mamba (DiFM) and Diffusion Scanning Permutation Mamba (DiPM) are tailored for temporal denoising and channel denoising during generation process, respectively.
• Figure 3: Architecture of proposed Mamba variants. Lag Fusion Mamba employs the LSF equation, while Permutation Scanning Mamba adopts the CPS equation.
• Figure 4: Matrix Visualizations. $\mathbf{M}$, $\mathbf{M}^{F}$, $\mathbf{M}^{C}$ denotes the matrices in Mamba, Lag Fusion Mamba and Permutation Scanning Mamba, respectively. $H$ is transformation matrix.
• Figure 5: Feature-based and population-level measures comparison on Energy (left) and KDD-Cup (right).