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.

Published as a conference paper at ICLR 2026 This involves capturing intricate temporal relationships and managing complex interdependencies across variables, both of which are essential for accurately modeling real-world time series patterns. Addressing these challenges is crucial for extending the capabilities of diffusion models to TSG.

Recent works on time series diffusion primarily focus on conditional generation tasks such as forecasting (Rasul et al., 2021;Shen & Kwok, 2023;Kollovieh et al., 2024) and imputation (Tashiro et al., 2021;Alcaraz & Strodthoff, 2022). For instance, TimeGrad (Rasul et al., 2021) employs recurrent neural networks to summarize history as conditions for denoising future values. Similarly, TimeDiff (Shen & Kwok, 2023) introduces autoregressive initialization and future mixup to enable efficient non-autoregressive prediction. CSDI (Tashiro et al., 2021) adopts self-supervised masking techniques, while Alcaraz & Strodthoff (2022) enhance CSDI by replacing transformers with structural state space models (Gu et al., 2021), improving long-range temporal modeling. These studies primarily focus on leveraging conditional information, designing robust conditioning networks, and constructing effective denoising architectures to address specific supervised tasks. In contrast, synthetic time series generation focuses on unconditionally producing high-quality time series (modeling the data distributions) that replicate the statistical properties of the original dataset (Ang et al., 2023).

Recent approaches to unconditional generation can be broadly divided into two categories. (i) Data-space diffusion models (