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Main Authors: He, Hengzhi, Xu, Shirong, Nemecek, Alexander, Li, Jiping, Ayday, Erman, Cheng, Guang
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2512.05333
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author He, Hengzhi
Xu, Shirong
Nemecek, Alexander
Li, Jiping
Ayday, Erman
Cheng, Guang
author_facet He, Hengzhi
Xu, Shirong
Nemecek, Alexander
Li, Jiping
Ayday, Erman
Cheng, Guang
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_05333
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Optimal Watermark Generation under Type I and Type II Errors
He, Hengzhi
Xu, Shirong
Nemecek, Alexander
Li, Jiping
Ayday, Erman
Cheng, Guang
Methodology
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.
title Optimal Watermark Generation under Type I and Type II Errors
topic Methodology
url https://arxiv.org/abs/2512.05333