# Theoretically Grounded Framework for LLM Watermarking: A Distribution-Adaptive Approach

arXiv: https://arxiv.org/abs/2410.02890 · HTML: https://mlsanity.com/paper/2410.02890/

## Key facts

- Cited by 22 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 41 of its 72 references that are in the map.
- First posted on arXiv 3 Oct 2024.

## 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, 30 of 41)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Multilingual Denoising Pre-training for Neural Machine Translation](https://mlsanity.com/paper/2001.08210/) (2020)
- [A Watermark for Large Language Models](https://mlsanity.com/paper/2301.10226/) (2023)
- [ELI5: Long Form Question Answering](https://mlsanity.com/paper/1907.09190/) (2019)
- [Robust Distortion-free Watermarks for Language Models](https://mlsanity.com/paper/2307.15593/) (2023)
- [Provable Robust Watermarking for AI-Generated Text](https://mlsanity.com/paper/2306.17439/) (2023)
- [Undetectable Watermarks for Language Models](https://mlsanity.com/paper/2306.09194/) (2023)
- [On the Reliability of Watermarks for Large Language Models](https://mlsanity.com/paper/2306.04634/) (2023)
- [Adversarial Watermarking Transformer: Towards Tracing Text Provenance with Data Hiding](https://mlsanity.com/paper/2009.03015/) (2020)
- [A Semantic Invariant Robust Watermark for Large Language Models](https://mlsanity.com/paper/2310.06356/) (2023)
- [A Survey of Text Watermarking in the Era of Large Language Models](https://mlsanity.com/paper/2312.07913/) (2023)
- [Unbiased Watermark for Large Language Models](https://mlsanity.com/paper/2310.10669/) (2023)
- [A Survey on LLM-Generated Text Detection: Necessity, Methods, and Future Directions](https://mlsanity.com/paper/2310.14724/) (2023)
- [Watermarks in the Sand: Impossibility of Strong Watermarking for Generative Models](https://mlsanity.com/paper/2311.04378/) (2023)
- [Three Bricks to Consolidate Watermarks for Large Language Models](https://mlsanity.com/paper/2308.00113/) (2023)
- [Robust Multi-bit Natural Language Watermarking through Invariant Features](https://mlsanity.com/paper/2305.01904/) (2023)
- [A Robust Semantics-based Watermark for Large Language Model against Paraphrasing](https://mlsanity.com/paper/2311.08721/) (2023)
- [REMARK-LLM: A Robust and Efficient Watermarking Framework for Generative Large Language Models](https://mlsanity.com/paper/2310.12362/) (2023)
- [Watermarking Text Generated by Black-Box Language Models](https://mlsanity.com/paper/2305.08883/) (2023)
- [Publicly-Detectable Watermarking for Language Models](https://mlsanity.com/paper/2310.18491/) (2023)
- [Adaptive Text Watermark for Large Language Models](https://mlsanity.com/paper/2401.13927/) (2024)
- [A Statistical Framework of Watermarks for Large Language Models: Pivot, Detection Efficiency and Optimal Rules](https://mlsanity.com/paper/2404.01245/) (2024)
- [WaterMax: breaking the LLM watermark detectability-robustness-quality trade-off](https://mlsanity.com/paper/2403.04808/) (2024)
- [Tracing Text Provenance via Context-Aware Lexical Substitution](https://mlsanity.com/paper/2112.07873/) (2021)
- [GumbelSoft: Diversified Language Model Watermarking via the GumbelMax-trick](https://mlsanity.com/paper/2402.12948/) (2024)

## Built on by (most cited first, 22 of 22)

- [Distributional Information Embedding: A Framework for Multi-bit Watermarking](https://mlsanity.com/paper/2501.16558/) (2025)
- [PASA: A Principled Embedding-Space Watermarking Approach for LLM-Generated Text under Semantic-Invariant Attacks](https://mlsanity.com/paper/2605.10977/) (2026)
- [On the Empirical Power of Goodness-of-Fit Tests in Watermark Detection](https://mlsanity.com/paper/2510.03944/) (2025)
- [A Reinforcement Learning Framework for Robust and Secure LLM Watermarking](https://mlsanity.com/paper/2510.21053/) (2025)
- [Watermarking Discrete Diffusion Language Models](https://mlsanity.com/paper/2511.02083/) (2025)
- [A Unified Framework for LLM Watermarks](https://mlsanity.com/paper/2602.06754/) (2026)
- [MirrorMark: Generalizable Mirrored Sampling for Multi-bit LLM Watermarking](https://mlsanity.com/paper/2601.22246/) (2026)
- [HeavyWater and SimplexWater: Distortion-Free LLM Watermarks for Low-Entropy Next-Token Predictions](https://mlsanity.com/paper/2506.06409/) (2025)
- [Boosting Adversarial Transferability via Commonality-Oriented Gradient Optimization](https://mlsanity.com/paper/2506.06992/) (2025)
- [Improving the Trade-off Between Watermark Strength and Speculative Sampling Efficiency for Language Models](https://mlsanity.com/paper/2602.01428/) (2026)
- [Watermark Forensics for Generative Models: An Information-Theoretic Perspective](https://mlsanity.com/paper/2607.13003/) (2026)
- [SAC-Copula: Quality-Preserving Watermarking for Diffusion Language Models via Smooth Correlated Gumbel Fields](https://mlsanity.com/paper/2608.20839/) (2026)
- [Functional Subspace Watermarking for Large Language Models](https://mlsanity.com/paper/2603.18793/) (2026)
- [Optimal Multi-bit Generative Watermarking Schemes Under Worst-Case False-Alarm Constraints](https://mlsanity.com/paper/2604.08759/) (2026)
- [Trustworthy AI: Ensuring Reliability and Accountability from Models to Agents](https://mlsanity.com/paper/2605.08964/) (2026)
- [Linguistics-Aware Non-Distortionary LLM Watermarking](https://mlsanity.com/paper/2606.00613/) (2026)
- [Stability-Aware Feature Design for Robust Watermark Detection in Machine-Generated Text](https://mlsanity.com/paper/2608.18102/) (2026)
- [Learning to Follow In-Context Watermark Instructions via Self-Distillation](https://mlsanity.com/paper/2608.29030/) (2026)
- [WoE Wrote It? Watermarking Mixture-of-Experts LLMs for Black-Box Text Provenance](https://mlsanity.com/paper/2608.29151/) (2026)
- [Invisible Ink, Visible Lies: How Production Watermarking Causes LLMs to Hallucinate](https://mlsanity.com/paper/2610.04860/) (2026)
- [SimpleMark: Fast Multi-Bit Text Watermarking under f -Divergence Constraints](https://mlsanity.com/paper/2610.05712/) (2026)
- [Pin It on Anyone: Certified Targeted Displacement of Multi-Bit LLM Watermarks Without the Key](https://mlsanity.com/paper/2610.18359/) (2026)

## Abstract (arXiv)

Watermarking has emerged as a crucial method to distinguish AI-generated text from human-created text. Current watermarking approaches often lack formal optimality guarantees or address the scheme and detector design separately. In this paper, we introduce a novel, unified theoretical framework for watermarking Large Language Models (LLMs) that jointly optimizes both the watermarking scheme and detector. Our approach aims to maximize detection performance while maintaining control over the worst-case false positive rate (FPR) and distortion on text quality. We derive closed-form optimal solutions for this joint design and characterize the fundamental trade-off between watermark detectability and distortion. Notably, we reveal that the optimal watermarking schemes should be adaptive to the LLM's generative distribution. Building on our theoretical insights, we propose a distortion-free, distribution-adaptive watermarking algorithm (DAWA) that leverages a surrogate model for model-agnosticism and efficiency. Experiments on Llama2-13B and Mistral-8×7B models confirm the effectiveness of our approach, particularly at ultra-low FPRs. Our code is available at https://github.com/yepengliu/DAWA.