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 data space, making latent-based watermarking incompatible. This creates the challenge of watermarking directly in data 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 temporal-feature data 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 while preserving robust watermark detectability. We extensively evaluate TimeWak on its impact on synthetic data quality, watermark detectability, and robustness under various post-editing attacks, against five 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 strongest state-of-the-art baseline, while remaining consistently detectable.

Generating temporal data under conditions is crucial for forecasting, imputation, and generative tasks. Such data often has metadata and partially observed signals that jointly influence the generated values. However, existing methods face three key limitations: (1) they condition on either the metadata or observed values, but rarely both together; (2) they adopt either training-time approaches that fail to generalise to unseen scenarios, or inference-time approaches that ignore metadata; and (3) they suffer from trade-offs between generation speed and temporal coherence across time windows, choosing either slow but coherent autoregressive methods or fast but incoherent parallel ones. We propose WaveStitch, a novel diffusion-based method to overcome these hurdles through: (1) dual-sourced conditioning on both metadata and partially observed signals; (2) a hybrid training-inference architecture, incorporating metadata during training and observations at inference via gradient-based guidance; and (3) a novel pipeline-style paradigm that generates time windows in parallel while preserving coherence through an inference-time conditional loss and a stitching mechanism. Across diverse datasets, WaveStitch demonstrates adaptability to arbitrary patterns of observed signals, achieving 1.81x lower mean-squared-error compared to the state-of-the-art, and generates data up to 166.48x faster than autoregressive methods while maintaining coherence. Our code is available at: https://github.com/adis98/WaveStitch.

Synthetic tabular data is crucial for sharing and augmenting data across silos, especially for enterprises with proprietary data. However, existing synthesizers are designed for centrally stored data. Hence, they struggle with real-world scenarios where features are distributed across multiple silos, necessitating on-premise data storage. We introduce SiloFuse, a novel generative framework for high-quality synthesis from cross-silo tabular data. To ensure privacy, SiloFuse utilizes a distributed latent tabular diffusion architecture. Through autoencoders, latent representations are learned for each client's features, masking their actual values. We employ stacked dis-tributed training to improve communication efficiency, reducing the number of rounds to a single step. Under SiloFuse, we prove the impossibility of data reconstruction for vertically partitioned synthesis and quantify privacy risks through three attacks using our benchmark framework. Experimental results on nine datasets showcase SiloFuse's competence against centralized diffusion-based synthesizers. Notably, SiloFuse achieves 43.8 and 29.8 higher percentage points over GANs in resemblance and utility. Experiments on communication show stacked training's fixed cost compared to the growing costs of end-to-end training as the number of training iterations increases. Additionally, SiloFuse proves robust to feature permutations and varying numbers of clients.