Diffusion models generate high-quality images but pose serious risks like copyright violation and disinformation. Watermarking is a key defense for tracing and authenticating AI-generated content. However, existing methods rely on threshold-based detection, which only supports fuzzy matching and cannot recover structured watermark data bit-exactly, making them unsuitable for offline verification or applications requiring lossless metadata (e.g., licensing instructions). To address this problem, in this paper, we propose Gaussian Shannon, a watermarking framework that treats the diffusion process as a noisy communication channel and enables both robust tracing and exact bit recovery. Our method embeds watermarks in the initial Gaussian noise without fine-tuning or quality loss. We identify two types of channel interference, namely local bit flips and global stochastic distortions, and design a cascaded defense combining error-correcting codes and majority voting. This ensures reliable end-to-end transmission of semantic payloads. Experiments across three Stable Diffusion variants and seven perturbation types show that Gaussian Shannon achieves state-of-the-art bit-level accuracy while maintaining a high true positive rate, enabling trustworthy rights attribution in real-world deployment. The source code have been made available at: https://github.com/Rambo-Yi/Gaussian-Shannon

翻译：扩散模型能够生成高质量的图像，但也带来了版权侵犯与虚假信息等严重风险。水印技术是对AI生成内容进行溯源与鉴定的关键防护手段。然而，现有方法依赖基于阈值的检测，仅支持模糊匹配，无法逐比特精确恢复结构化水印数据，因此不适用于离线验证或需要无损元数据（例如许可指令）的应用场景。针对这一问题，本文提出高斯香农——一个将扩散过程视为噪声通信信道的水印框架，既能实现鲁棒溯源，又能支持精确比特恢复。该方法将水印嵌入初始高斯噪声中，无需微调或牺牲生成质量。我们识别出两类信道干扰，即局部比特翻转与全局随机畸变，并设计了一种结合纠错编码与多数投票的级联防御机制，从而确保语义载荷的端到端可靠传输。在三种Stable Diffusion变体及七种扰动类型上的实验表明，高斯香农在保持高真阳率的同时，实现了最先进的比特级精度，能够在实际部署中实现可信的权利归属。源代码已开源至：https://github.com/Rambo-Yi/Gaussian-Shannon