S2S-Diff: Structure-to-Signal Diffusion Models for Time Series Synthesis

Time-series synthesis is fundamental to simulation, data augmentation, and privacy-preserving data sharing. Despite recent advances in generative modeling, most approaches generate sequences directly in high-dimensional data or latent spaces without modeling an explicit structural representation, limiting interpretability and controllability. To address this limitation, we propose S2S-Diff, a structure-to-signal cascaded diffusion model that synthesizes time series through sparse structural composition. S2S-Diff represents each sequence as a sparse atom-set composition over a learned multi-scale structural dictionary, where the active atoms summarize the dominant structural characteristics of the sequence. Generative modeling is performed in this compact structural space, and sampled structural compositions condition a diffusion model for signal realization. By decoupling high-level structural composition from fine-grained signal realization, S2S-Diff reduces the complexity of generative modeling while introducing an explicit structural inductive bias and preserving stochastic flexibility. Experiments across diverse benchmarks show that S2S-Diff achieves strong synthesis quality while maintaining structural sparsity and controllability. These findings support structural abstraction as a principled basis for interpretable and controllable time-series synthesis.