On the Information-Theoretic Limits of Latent-Space Watermarking Through Pretrained Generators

Jinwan Jeon, Minju Lee, Sung Hoon Lim

We study latent-space watermarking through a pretrained generator using a prescribed latent-to-output stochastic mapping, called the renderer. A watermark encoder selects the latent input using a message and secret key. For every message and semantic context, the released output must have exactly the desired conditional output distribution. For finite alphabets, we derive rate--key inner and outer bounds and characterize the coding and coordination requirements for realizing watermark communication through the prescribed latent interface. When the target output distribution of the generator uniquely determines the corresponding latent input distribution through the renderer, a strengthened converse yields the capacity region; the same region governs explicit preservation of the pretrained latent distribution. We extend the analysis to general jointly Gaussian models and identify a sufficient statistic of the latent that captures both the watermark-bearing information available at the generated output and the latent coordination required to preserve its target distribution. For the vector Gaussian model, we further characterize the optimal allocation of the secret-key resource…