Correlation-Aware and Gaussianity-Preserving Robust Latent Angular Watermarking for Diffusion Models

2026-07-24

AI Summary

This work addresses critical limitations in existing latent-domain watermarking methods for diffusion models, which degrade generation quality by violating the Gaussianity of latent variables, exhibiting sensitivity to perturbations, and disregarding the induced violation of the i.i.d. assumption that leads to undesirable correlations. To overcome these issues, we propose Latent Angular Watermarking (LAW), which encodes watermark bits as epipolar angles (±π/2) between pairs of latent variables, leveraging the rotational invariance of isotropic Gaussian distributions to enable robust embedding while preserving Gaussianity. We further introduce an amplitude-driven variant, LAW-M, to enhance stability. Our theoretical analysis rigorously characterizes the post-watermarking correlation structure, proving that non-zero correlations arise only in sparse, structured off-diagonal entries. Moreover, we establish that the variance of detection angle error scales inversely with the squared norm of latent pairs (var(Δφ) ∝ 1/ρ²), achieving a principled trade-off between generation fidelity and robustness against attacks.

Abstract

Latent domain watermarking for diffusion models embeds watermarks directly into the latent prior, enjoying non-intrusiveness to model parameters and seamless integration with the generation process. However, due to the violation of latent Gaussianity or sensitivity to normal and malicious perturbations during latent inversion, existing methods are prone to watermark detection or removal attacks. A further overlooked problem is the violation of the i.i.d. latent condition after watermarking, which leads to latent correlation degradation and generation fidelity loss. Although this has been externally measured by FID, the internal correlation structure has yet to be rigorously characterized. To address the above issues, and motivated by the rotation-invariant property of isotropic Gaussian, we propose \textit{Latent Angular Watermarking (LAW)}, which encodes watermark bits as antipodal angles ($\pmπ/2$ relative to a reference pair) between disjoint pairs of latent elements while preserving the Gaussianity. The antipodal ($π$-separation) encoding maximizes geometric separation between bit values, and we prove that the decoding angular-error variance is proportional to the norm of the latent pair, i.e., $\operatorname{var}(Δφ) \propto 1/ρ^2$. We further propose a magnitude-driven variant, LAW-M, which anchors watermark bits in the most geometrically stable latent dimensions, yielding additional robustness gains. Theoretically, we provide a rigorous characterization of the induced correlation degradation, deriving in closed form the autocorrelation structure of the watermarked latent and proving that correlations are confined to a sparse, structured set of off-diagonal elements with fixed $\pmπ/4$ values.

Problem

• latent watermarking
• Gaussianity preservation
• correlation degradation
• diffusion models
• i.i.d. violation

Innovation

• Latent Angular Watermarking
• Gaussianity Preservation
• Correlation-Aware
• Diffusion Models
• Robust Watermarking