TimeWak: Temporal Chained-Hashing Watermark for Time Series Data

2025-06-06

AI Summary

This work addresses the challenge of embedding traceable watermarks into multivariate time series generated by diffusion models within the real data space. We propose a novel watermarking framework that jointly accounts for feature heterogeneity and temporal dependencies. Our approach introduces a pioneering temporal chained-hashing watermarking mechanism and designs an ε-precise reverse process to model the non-uniform distribution of multivariate diffusion reconstruction errors, enabling robust watermark detection under bounded error constraints. The method integrates real-space temporal feature embedding, chained-hashing structure, and reverse-process error analysis. Evaluated on five benchmark datasets, it achieves a 61.96% improvement in contextual FID and an 8.44% gain in correlation score over state-of-the-art methods. The embedded watermark demonstrates high resilience against post-generation editing attacks—including cropping, interpolation, and noise injection—while maintaining reliable detectability.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Time-Series/Data Streams
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust

Application Category

• Security and Privacy: Data transparency and provenance
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

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.

Problem

• Watermarking synthetic time series in real space
• Handling temporal dependencies and feature heterogeneity
• Ensuring high detectability and data utility

Innovation

• Embeds watermark in real temporal-feature space
• Uses temporal chained-hashing for watermarking
• Implements ε-exact inversion for error distribution