TimeWak: Temporal Chained-Hashing Watermark for Time Series Data

Synthetic time series generated by diffusion models enable sharing privacy-sensitive datasets, such as patients' functional MRI records. Key criteria for synthetic data include high data utility and traceability to verify the data source. Recent watermarking methods embed in homogeneous latent spaces, but state-of-the-art time series generators operate in real space, making latent-based watermarking incompatible. This creates the challenge of watermarking directly in real space while handling feature heterogeneity and temporal dependencies. We propose TimeWak, the first watermarking algorithm for multivariate time series diffusion models. To handle temporal dependence and spatial heterogeneity, TimeWak embeds a temporal chained-hashing watermark directly within the real temporal-feature space. The other unique feature is the $\epsilon$-exact inversion, which addresses the non-uniform reconstruction error distribution across features from inverting the diffusion process to detect watermarks. We derive the error bound of inverting multivariate time series and further maintain high watermark detectability. We extensively evaluate TimeWak on its impact on synthetic data quality, watermark detectability, and robustness under various post-editing attacks, against 5 datasets and baselines of different temporal lengths. Our results show that TimeWak achieves improvements of 61.96% in context-FID score, and 8.44% in correlational scores against the state-of-the-art baseline, while remaining consistently detectable.

Federated Time Series Generation on Feature and Temporally Misaligned Data

Distributed time series data presents a challenge for federated learning, as clients often possess different feature sets and have misaligned time steps. Existing federated time series models are limited by the assumption of perfect temporal or feature alignment across clients. In this paper, we propose FedTDD, a novel federated time series diffusion model that jointly learns a synthesizer across clients. At the core of FedTDD is a novel data distillation and aggregation framework that reconciles the differences between clients by imputing the misaligned timesteps and features. In contrast to traditional federated learning, FedTDD learns the correlation across clients' time series through the exchange of local synthetic outputs instead of model parameters. A coordinator iteratively improves a global distiller network by leveraging shared knowledge from clients through the exchange of synthetic data. As the distiller becomes more refined over time, it subsequently enhances the quality of the clients' local feature estimates, allowing each client to then improve its local imputations for missing data using the latest, more accurate distiller. Experimental results on five datasets demonstrate FedTDD's effectiveness compared to centralized training, and the effectiveness of sharing synthetic outputs to transfer knowledge of local time series. Notably, FedTDD achieves 79.4% and 62.8% improvement over local training in Context-FID and Correlational scores.