On the Intrinsic Limited Robustness of Latent-Based Watermarking

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.