As generative models enable rapid creation of high-fidelity images, societal concerns about misinformation and authenticity have intensified. A promising remedy is multi-bit image watermarking, which embeds a multi-bit message into an image so that a verifier can later detect whether the image is generated by someone and further identify the source by decoding the embedded message. Existing approaches often fall short in capacity, resilience to common image distortions, and theoretical justification. To address these limitations, we propose ADD (Add, Dot, Decode), a multi-bit image watermarking method with two stages: learning a watermark to be linearly combined with the multi-bit message and added to the image, and decoding through inner products between the watermarked image and the learned watermark. On the standard MS-COCO benchmark, we demonstrate that for the challenging task of 48-bit watermarking, ADD achieves 100\% decoding accuracy, with performance dropping by at most 2\% under a wide range of image distortions, substantially smaller than the 14\% average drop of state-of-the-art methods. In addition, ADD achieves substantial computational gains, with 2-fold faster embedding and 7.4-fold faster decoding than the fastest existing method. We further provide a theoretical analysis explaining why the learned watermark and the corresponding decoding rule are effective.

翻译：随着生成模型能够快速创建高保真图像，社会对信息真实性与虚假信息的担忧日益加剧。一种有前景的解决方案是多比特图像水印技术，它通过将多比特信息嵌入图像，使得验证者能够检测该图像是否由特定来源生成，并通过解码嵌入信息进一步溯源。现有方法在容量、对常见图像失真的鲁棒性及理论依据方面常存在不足。为突破这些局限，我们提出ADD（嵌入-点积-解码）方法，这是一种两阶段多比特图像水印方案：首先学习一个水印，将其与多比特消息进行线性组合后叠加至图像；随后通过水印图像与学习所得水印的内积实现解码。在标准MS-COCO基准测试中，面对48比特水印的严峻挑战，ADD方法实现了100%的解码准确率，且在多种图像失真条件下性能下降幅度不超过2%，显著优于现有最优方法平均14%的性能衰减。此外，ADD在计算效率上取得显著提升，嵌入速度较现有最快方法提升2倍，解码速度提升7.4倍。我们进一步通过理论分析揭示了所学习水印及其对应解码规则的有效性原理。