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TimeWak: Temporal Chained-Hashing Watermark for Time Series Data

NeurIPS 2025 · Time series › Causal and generative time series · approach: State-space and latent dynamics forecasting · 1 citations (OpenAlex)

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Proposes TimeWak, a generation-time watermark for multivariate time series diffusion models that embeds temporally chained-hashed seeds in data space and detects them via epsilon-exact BDIA-DDIM inversion.

Problem

Watermarking synthetic multivariate time series produced by data-space diffusion models, where latent-space watermarks are inapplicable and feature heterogeneity and temporal dependence make detection hard under lossy diffusion inversion.

Approach

Embed watermark seeds as temporally chained hashes along the time axis, shuffle them per feature, map them to initial Gaussian noise, and detect by inverting a BDIA-DDIM sampler with a bounded inversion error (epsilon-exact inversion) and checking hash consistency.

Key results

• TimeWak improves Context-FID by 61.96% on MuJoCo versus the strongest baseline TabWak-transposed.
• TimeWak improves correlational score by 8.44% on fMRI and reaches TPR 1.0 at 0.1% FPR on 64-length sequences with one or two samples.
• Under post-editing attacks TimeWak keeps the best Z-scores in most settings, e.g., 375.96 under 5% offset on Stocks, while TabWak variants and HTW degrade.

Measured effects reported in the paper

Surprising findings

• Tree-Ring's detection scores increase under some post-processing attacks such as random cropping and min-max insertion.
• HTW sometimes beats un-watermarked data on quality metrics, possibly because its perturbations move samples closer to ground truth, yet it has low Z-scores.

Limitations

• Does not natively support streaming data; requires windowed processing.
• Per-timestep watermarking remains unexplored.
• Epsilon-exact inversion is an approximation that sets x1 to x0, so inversion is not exact.

Experimental setup

Datasets: Stocks ETTh MuJoCo Energy fMRI

Benchmarks: Stocks ETTh MuJoCo Energy fMRI

Metrics: Context-FID Correlational score Discriminative score Predictive score Z-score TPR@0.1%FPR

Baselines: Tree-Ring Gaussian Shading TabWak TabWak-transposed Heads Tails Watermark

Builds on: Diffusion-TS DDIM BDIA Gaussian Shading TabWak

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