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

arXiv: https://arxiv.org/abs/2609.24377 · HTML: https://mlsanity.com/paper/2609.24377/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Watermarking generated content and models, one of 12 directions in LLM safety and security.
- Builds on 21 of its 43 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Placed in

- LLM safety and security / [Watermarking generated content and models](https://mlsanity.com/safety/watermarking-generated-content-and-models/)

## Builds on (most cited first, 21 of 21)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [A Watermark for Large Language Models](https://mlsanity.com/paper/2301.10226/) (2023)
- [HiDDeN: Hiding Data With Deep Networks](https://mlsanity.com/paper/1807.09937/) (2018)
- [Robust Distortion-free Watermarks for Language Models](https://mlsanity.com/paper/2307.15593/) (2023)
- [The Stable Signature: Rooting Watermarks in Latent Diffusion Models](https://mlsanity.com/paper/2303.15435/) (2023)
- [StegaStamp: Invisible Hyperlinks in Physical Photographs](https://mlsanity.com/paper/1904.05343/) (2019)
- [Undetectable Watermarks for Language Models](https://mlsanity.com/paper/2306.09194/) (2023)
- [Tree-Ring Watermarks: Fingerprints for Diffusion Images that are Invisible and Robust](https://mlsanity.com/paper/2305.20030/) (2023)
- [Gaussian Shading: Provable Performance-Lossless Image Watermarking for Diffusion Models](https://mlsanity.com/paper/2404.04956/) (2024)
- [Invisible Image Watermarks Are Provably Removable Using Generative AI](https://mlsanity.com/paper/2306.01953/) (2023)
- [WAVES: Benchmarking the Robustness of Image Watermarks](https://mlsanity.com/paper/2401.08573/) (2024)
- [RingID: Rethinking Tree-Ring Watermarking for Enhanced Multi-Key Identification](https://mlsanity.com/paper/2404.14055/) (2024)
- [An Undetectable Watermark for Generative Image Models](https://mlsanity.com/paper/2410.07369/) (2024)
- [Perfectly Secure Steganography Using Minimum Entropy Coupling](https://mlsanity.com/paper/2210.14889/) (2022)
- [LaWa: Using Latent Space for In-Generation Image Watermarking](https://mlsanity.com/paper/2408.05868/) (2024)
- [The Rate-Distortion-Perception Tradeoff: The Role of Common Randomness](https://mlsanity.com/paper/2202.04147/) (2022)
- [Optimized Couplings for Watermarking Large Language Models](https://mlsanity.com/paper/2505.08878/) (2025)
- [FARI: Robust One-Step Inversion for Watermarking in Diffusion Models](https://mlsanity.com/paper/2607.26723/) (2026)

## Abstract (arXiv)

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 across the resulting modes. Finally, we turn to an emerging robustness threat that is particularly natural in generative watermarking: an adversary can regenerate the released sample to obtain a fresh realization of the same underlying content while attenuating or destroying the embedded watermark. We incorporate this robustness axis into our framework and characterize the one-pass compound capacity of the scalar Gaussian model when the semantic context is known to the encoder but hidden from the detector, while the regeneration attack may depend on that context. Extending the analysis to multiple rounds of repeated canonical regeneration, we characterize the resulting watermark-capacity decay.