Latent-to-Data Cascaded Diffusion Models for Unconditional Time Series Generation

Synthetic time series generation (TSG) is crucial for applications such as privacy preservation, data augmentation, and anomaly detection. A key challenge in TSG lies in modeling the multi-modal distributions of time series, which requires simultaneously capturing diverse high-level representation distributions and preserving local temporal fidelity. Most existing diffusion models, however, are constrained by their single-space focus: latent-space models capture representation distributions but often compromise local fidelity, while data-space models preserve local details in the data space but struggle to learn high-level representations essential for multi-modal time series. To address these limitations, we propose L2D-Diff, a dual-space diffusion framework for synthetic time series generation. Specifically, L2D-Diff first compresses input sequences into a latent space to efficiently model the distribution of time series representations. The distribution then guides a data-space diffusion model to refine local data details, enabling faithful generation of time series distribution without relying on external conditions. Experiments on both single-modal and multi-modal datasets demonstrate the effectiveness of L2D-Diff in tackling unconditional TSG tasks. Ablation studies further highlight the necessity and impact of its dual-space design, showcasing its capability to achieve representation coherence and local fidelity.