# TimeWak: Temporal Chained-Hashing Watermark for Time Series Data

arXiv: https://arxiv.org/abs/2506.06407 · HTML: https://mlsanity.com/paper/2506.06407/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Robustness, privacy and adversarial aspects, one of 14 directions in Diffusion models.
- Builds on 31 of its 42 references that are in the map.
- First posted on arXiv 6 Jun 2025.

## Placed in

- Diffusion models / [Robustness, privacy and adversarial aspects](https://mlsanity.com/diffusion/robustness-privacy-and-adversarial-aspects/)

## Builds on (most cited first, 30 of 31)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [TS2Vec: Towards Universal Representation of Time Series](https://mlsanity.com/paper/2106.10466/) (2021)
- [dm_control: Software and Tasks for Continuous Control](https://mlsanity.com/paper/2006.12983/) (2020)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [The Stable Signature: Rooting Watermarks in Latent Diffusion Models](https://mlsanity.com/paper/2303.15435/) (2023)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Tree-Ring Watermarks: Fingerprints for Diffusion Images that are Invisible and Robust](https://mlsanity.com/paper/2305.20030/) (2023)
- [Mixed-Type Tabular Data Synthesis with Score-based Diffusion in Latent Space](https://mlsanity.com/paper/2310.09656/) (2023)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [Robust Invisible Video Watermarking with Attention](https://mlsanity.com/paper/1909.01285/) (2019)
- [Gaussian Shading: Provable Performance-Lossless Image Watermarking for Diffusion Models](https://mlsanity.com/paper/2404.04956/) (2024)
- [Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement](https://mlsanity.com/paper/2301.03028/) (2023)
- [Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2307.11494/) (2023)
- [Diffusion Models for Time Series Applications: A Survey](https://mlsanity.com/paper/2305.00624/) (2023)
- [PSA-GAN: Progressive Self Attention GANs for Synthetic Time Series](https://mlsanity.com/paper/2108.00981/) (2021)
- [Exact Diffusion Inversion via Bi-directional Integration Approximation](https://mlsanity.com/paper/2307.10829/) (2023)
- [ScoreGrad: Multivariate Probabilistic Time Series Forecasting with Continuous Energy-based Generative Models](https://mlsanity.com/paper/2106.10121/) (2021)
- [Watermarking Diffusion Model](https://mlsanity.com/paper/2305.12502/) (2023)
- [Generative AI for Synthetic Data Generation: Methods, Challenges and the Future](https://mlsanity.com/paper/2403.04190/) (2024)
- [TSGBench: Time Series Generation Benchmark](https://mlsanity.com/paper/2309.03755/) (2023)
- [Regular Time-series Generation using SGM](https://mlsanity.com/paper/2301.08518/) (2023)
- [A Transformer-based Diffusion Probabilistic Model for Heart Rate and Blood Pressure Forecasting in Intensive Care Unit](https://mlsanity.com/paper/2301.06625/) (2023)
- [Duwak: Dual Watermarks in Large Language Models](https://mlsanity.com/paper/2403.13000/) (2024)
- [SiloFuse: Cross-silo Synthetic Data Generation with Latent Tabular Diffusion Models](https://mlsanity.com/paper/2404.03299/) (2024)

## Built on by (most cited first, 3 of 3)

- [TimeGuard: Channel-wise Pool Training for Backdoor Defense in Time Series Forecasting](https://mlsanity.com/paper/2605.22365/) (2026)
- [Detecting Diffusion-Generated Time Series Under Generator Shift](https://mlsanity.com/paper/2605.28355/) (2026)
- [A Locally Tokenized Generative Model for Robust Time-Series Watermarking](https://mlsanity.com/paper/2608.19727/) (2026)

## Abstract (arXiv)

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 ε-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.