# The Coding Limits of Robust Watermarking for Generative Models

arXiv: https://arxiv.org/abs/2509.10577 · HTML: https://mlsanity.com/paper/2509.10577/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Watermarking generated content and models, one of 12 directions in LLM safety and security.
- Builds on 23 of its 51 references that are in the map.
- First posted on arXiv 11 Sep 2025.

## 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, 23 of 23)

- [A Watermark for Large Language Models](https://mlsanity.com/paper/2301.10226/) (2023)
- [Paraphrasing evades detectors of AI-generated text, but retrieval is an effective defense](https://mlsanity.com/paper/2303.13408/) (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)
- [Undetectable Watermarks for Language Models](https://mlsanity.com/paper/2306.09194/) (2023)
- [Artificial Fingerprinting for Generative Models: Rooting Deepfake Attribution in Training Data](https://mlsanity.com/paper/2007.08457/) (2020)
- [Tree-Ring Watermarks: Fingerprints for Diffusion Images that are Invisible and Robust](https://mlsanity.com/paper/2305.20030/) (2023)
- [A Recipe for Watermarking Diffusion Models](https://mlsanity.com/paper/2303.10137/) (2023)
- [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)
- [Watermarks in the Sand: Impossibility of Strong Watermarking for Generative Models](https://mlsanity.com/paper/2311.04378/) (2023)
- [Robustness of AI-Image Detectors: Fundamental Limits and Practical Attacks](https://mlsanity.com/paper/2310.00076/) (2023)
- [An Undetectable Watermark for Generative Image Models](https://mlsanity.com/paper/2410.07369/) (2024)
- [Publicly-Detectable Watermarking for Language Models](https://mlsanity.com/paper/2310.18491/) (2023)
- [Generating Steganographic Images via Adversarial Training](https://mlsanity.com/paper/1703.00371/) (2017)
- [Leveraging Optimization for Adaptive Attacks on Image Watermarks](https://mlsanity.com/paper/2309.16952/) (2023)
- [Pseudorandom Error-Correcting Codes](https://mlsanity.com/paper/2402.09370/) (2024)
- [Supervised GAN Watermarking for Intellectual Property Protection](https://mlsanity.com/paper/2209.03466/) (2022)
- [UnMarker: A Universal Attack on Defensive Image Watermarking](https://mlsanity.com/paper/2405.08363/) (2024)
- [Revealing Weaknesses in Text Watermarking Through Self-Information Rewrite Attacks](https://mlsanity.com/paper/2505.05190/) (2025)
- [Securing Deep Generative Models with Universal Adversarial Signature](https://mlsanity.com/paper/2305.16310/) (2023)
- [Ideal Pseudorandom Codes](https://mlsanity.com/paper/2411.05947/) (2024)

## Built on by (most cited first, 2 of 2)

- [Removing the Watermark Is Not Enough: Forensic Stealth in Generative-AI Watermark Removal](https://mlsanity.com/paper/2605.09203/) (2026)
- [Watermark Forensics for Generative Models: An Information-Theoretic Perspective](https://mlsanity.com/paper/2607.13003/) (2026)

## Abstract (arXiv)

We study a basic question about cryptographic watermarking for generative models: how reliable can a watermark remain when an adversary is allowed to corrupt the encoded signal? To address this question, we introduce a minimal coding abstraction that we call a zero-bit tamper-detection code. This is a secret-key procedure that samples a pseudorandom codeword and, given a candidate word, decides whether it should be treated as unmarked content or as the result of tampering with a valid codeword. It captures the two core requirements of robust watermarking: soundness and tamper detection. Within this abstraction we prove a sharp unconditional limit on robustness to independent symbol corruption. For an alphabet of size q, there is a critical corruption rate of 1-1/q such that no scheme with soundness, even relaxed to allow a fixed constant false positive probability on random content, can reliably detect tampering once an adversary can change more than this fraction of symbols. In particular, in the binary case no cryptographic watermark can remain robust if more than half of the encoded bits are modified. We also show that this threshold is tight by giving simple information-theoretic constructions that achieve soundness and tamper detection for all strictly smaller corruption rates. We then test experimentally whether this limit appears in practice by looking at the recent watermarking for images of Gunn, Zhao, and Song (ICLR 2025). We show that a simple crop and resize operation reliably flipped about half of the latent signs and consistently prevented belief-propagation decoding from recovering the codeword, erasing the watermark while leaving the image visually intact.