We consider the problem of securely and robustly embedding covert messages into an image-based diffusion model's output. The sender and receiver want to exchange the maximum amount of information possible per diffusion sampled image while remaining undetected. The adversary wants to detect that such communication is taking place by identifying those diffusion samples that contain covert messages. To maximize robustness to transformations of the diffusion sample, a strategy is for the sender and the receiver to embed the message in the initial latents. We first show that prior work that attempted this is easily broken because their embedding technique alters the latents' distribution. We then propose a straightforward method to embed covert messages in the initial latent {\em without} altering the distribution. We prove that our construction achieves indistinguishability to any probabilistic polynomial time adversary. Finally, we discuss and analyze empirically the tradeoffs between embedding capacity, message recovery rates, and robustness. We find that optimizing the inversion method for error correction is crucial for reliability.

翻译：本文研究了在基于图像的扩散模型输出中安全且鲁棒地嵌入隐蔽消息的问题。发送方和接收方希望在每张扩散采样图像中交换尽可能多的信息，同时保持不被检测。对手则试图通过识别那些包含隐蔽消息的扩散样本来检测此类通信的存在。为了最大化对扩散样本变换的鲁棒性，一种策略是发送方和接收方将消息嵌入到初始潜在变量中。我们首先证明，先前尝试此方法的研究很容易被攻破，因为其嵌入技术改变了潜在变量的分布。随后，我们提出了一种在初始潜在变量中嵌入隐蔽消息的简单方法，且不改变其分布。我们证明了我们的构造对于任何概率多项式时间对手都具有不可区分性。最后，我们讨论并实证分析了嵌入容量、消息恢复率和鲁棒性之间的权衡。我们发现，为纠错优化反演方法对可靠性至关重要。