# Optimal Watermark Generation under Type I and Type II Errors

arXiv: https://arxiv.org/abs/2512.05333 · HTML: https://mlsanity.com/paper/2512.05333/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2025.

## Built on by (most cited first, 3 of 3)

- [Watermark Forensics for Generative Models: An Information-Theoretic Perspective](https://mlsanity.com/paper/2607.13003/) (2026)
- [Auditing Cross-Lingual Fairness in Language Model Watermarking](https://mlsanity.com/paper/2608.20047/) (2026)
- [Watermarks Without Verification: AI Text Watermarking After the EU AI Act](https://mlsanity.com/paper/2609.09604/) (2026)

## Abstract (arXiv)

Watermarking has recently emerged as a crucial tool for protecting the intellectual property of generative models and for distinguishing AI-generated content from human-generated data. Despite its practical success, most existing watermarking schemes are empirically driven and lack a theoretical understanding of the fundamental trade-off between detection power and generation fidelity. To address this gap, we formulate watermarking as a statistical hypothesis testing problem between a null distribution and its watermarked counterpart. Under explicit constraints on false-positive and false-negative rates, we derive a tight lower bound on the achievable fidelity loss, measured by a general f-divergence, and characterize the optimal watermarked distribution that attains this bound. We further develop a corresponding sampling rule that provides an optimal mechanism for inserting watermarks with minimal fidelity distortion. Our result establishes a simple yet broadly applicable principle linking hypothesis testing, information divergence, and watermark generation.