Ordinary differential equation (ODE)-based diffusion models enable deterministic image synthesis, establishing a reversible mapping suitable for generative steganography. While prevailing methods strictly adhere to a standard normal prior, empirical evidence indicates that controlled deviations from this distribution reduce numerical inversion errors without compromising perceptual quality. Leveraging this observation, the Approximate Gaussian Mapping (AGM) is proposed as a linear transformation strategy that embeds secrets by modulating noise scale and variance. To balance retrieval numerical consistence and security, a two-stage decoupled optimization strategy is introduced to minimize the Kullback-Leibler divergence subject to target bit accuracy constraints. Beyond the proposed method, we conduct a mechanistic analysis of the divergent behaviors between pixel-space and latent-space architectures. The experimental results reveal that the VAE encoder enhances robustness by filtering external perturbations, whereas the structural regularization of the VAE decoder and the semantic variance introduced by text prompts jointly mask embedding artifacts to improve security. Experimental results confirm that pixel-space mplementations maximize embedding capacity for lossless channels, while latent-space approaches offer superior robustness and security suitable for adversarial environments

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