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This paper theoretically analyzes latent-based watermarking for diffusion models, revealing that existing methods overestimate robustness to geometric transformations (RST) due to inherent limitations in the latent embedding domain. The authors derive a maximum perturbation bound linking pixel-space and latent-space effects and formulate practical detection mechanisms, empirically validating that the current paradigm intrinsically limits robustness. These findings provide analytical tools and design guidelines for future, more robust watermarking techniques.
Latent-based diffusion model watermarking is fundamentally brittle to geometric distortions, with a theoretically derived perturbation bound explaining its limited robustness.
Existing latent-based watermarking methods for diffusion models have overestimated their robustness to image distortions, including geometric transformations such as rotation, scaling, and translation (RST). Moreover, this paradigm of watermarking approaches may suffer from inherent limitations arising from the domain in which the watermark is embedded. In this paper, we provide the first theoretical analysis explaining why these methods lack invariance to perturbations. By relaxing the invariant relation, we derive a maximum perturbation bound that characterizes the relationship between pixel-space perturbations and their corresponding effects in latent space. In addition, we present the first analytical formulation that captures all components of practical detection mechanisms. Finally, we conduct experiments to validate the theoretical findings and the limitations of latent-based watermarking methods. Our theoretical and empirical results indicate that, under the current design paradigm, latent-based watermarking methods intrinsically exhibit limited robustness. We conclude by providing the analytical tool and design guidelines that future research could follow.
