Generative image steganography has attracted significant attention for its exceptional resistance to steganalysis. However, current generative steganography methods still face limitations in terms of the lack of provable security guarantees under statistical analysis and vulnerability to real-world, unforeseen channel attacks. To address these issues, this paper proposes a novel generative image steganography framework that leverages the Latent Diffusion Model (LDM). Notably, we have uncover a consistent trend: regardless of whether an image has undergone attacks such as compression or noise addition, the sign pattern of values in its latent vector encoded by the LDM remains largely invariant. Capitalizing on this trend, we have devised an adaptive distribution-preserving mapping (ADPM) mechanism, capable of converting a secret message into a latent vector that follows standard normal distribution in an adjustable way. Since both the secret latent vector and the latent vector randomly generated during regular image generation follow the same distribution, satisfying the optimal input conditions for the diffusion model, the proposed method can achieve provable security. Experimental results demonstrate the outstanding performance of our approach in terms of robustness, security, and extraction accuracy.

In recent years, generative steganography has witnessed remarkable progress in the field of covert communication. It leverages techniques such as generative adversarial networks (GANs) or flow-based generative models (GLOW) to generate stego images. However, these approaches often grapple with the dilemma of achieving optimal steganographic capacity while ensuring the accurate extraction of hidden information. Additionally, the models occasionally still generate low-quality images that are highly vulnerable to detection by steganalysis tools. To tackle the aforementioned challenges and enhance the overall performance of generative image steganography, this paper proposes the deterministic guided additive diffusion model for generative image steganography (DGADM-GIS). Initially, we devise a reversible mapping function that is used for deterministic guided by a provided secret message, and then construct a secret latent Gaussian vector. Moreover, the proposed DGADM-GIS framework designs an additive sampling method based on the superposition principle of normal distribution to obtain a Gaussian vector that satisfies independent, random and obeys the standard normal distribution, which is transformed to a stego image in a way of maintaining the distribution by the diffusion model. Furthermore, we conduct error analysis experiments on our proposed scheme and derive methods to enhance the accuracy of secret information extraction. The experimental results show that our proposed steganographic method exhibits robust resistance to steganalysis. When embedding 3 bits of secret information per pixel, it achieves nearly 100% extraction accuracy.