Diffusion model-based generative image steganography (DM-GIS) is an emerging paradigm that leverages the generative power of diffusion models to conceal secret messages without requiring pre-existing cover images. In this paper, we identify a fundamental trade-off between stego image quality, steganographic security, and extraction reliability within the DM-GIS framework. Drawing on this insight, we propose \textbf{PA-B2G}, a \textbf{P}rovable and \textbf{A}djustable \textbf{B}it-to-\textbf{G}aussian mapping. Theoretically, PA-B2G guarantees the reversible encoding of arbitrary-length bit sequences into pure Gaussian noise; practically, it enables fine-grained control over the balance between image fidelity, security, and extraction accuracy. By integrating PA-B2G with probability-flow ordinary differential equations (PF-ODEs), we establish a theoretically invertible mapping between secret bitstreams and stego images. PA-B2G is model-agnostic and can be seamlessly integrated into mainstream diffusion models without additional training or fine-tuning, making it also suitable for diffusion model watermarking. Extensive experiments validate our theoretical analysis of the inherent DM-GIS trade-offs and demonstrate that our method flexibly supports arbitrary payloads while achieving competitive image quality and security. Furthermore, our method exhibits strong resilience to lossy processing in watermarking applications, highlighting its practical utility.

翻译：基于扩散模型的生成式图像隐写术是一种新兴范式，它利用扩散模型的生成能力来隐藏秘密信息，无需依赖预先存在的载体图像。本文揭示了DM-GIS框架中隐写图像质量、隐写安全性与信息提取可靠性之间的基本权衡关系。基于这一洞察，我们提出了**PA-B2G**，一种**可证明且可调节的比特-高斯映射**方法。理论上，PA-B2G保证了任意长度比特序列可逆编码为纯高斯噪声；实践中，它实现了对图像保真度、安全性与提取精度之间平衡的细粒度控制。通过将PA-B2G与概率流常微分方程相结合，我们在秘密比特流与隐写图像之间建立了理论可逆的映射关系。PA-B2G具有模型无关性，无需额外训练或微调即可无缝集成到主流扩散模型中，这也使其适用于扩散模型水印任务。大量实验验证了我们对DM-GIS内在权衡关系的理论分析，并证明该方法在支持任意载荷的同时，实现了具有竞争力的图像质量与安全性。此外，该方法在水印应用中表现出对有损处理的强鲁棒性，凸显了其实用价值。