Optimal Watermark Generation under Type I and Type II Errors

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ID: 324715
2026
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Abstract
Abstract 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.
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openalex_W4417142420 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Hengzhi He, Shirong Xu, Alexander Nemecek, J. Li, Erman Ayday, Guang Cheng
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Journal jurnal biometrika dan kependudukan
Year 2026
DOI
10.1093/biomet/asag049
URL
https://doi.org/10.1093/biomet/asag049
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