Distribution-Preserving Latent Image Steganography via Conditional Optimal Transport and Theoretical Target Synthesis

We propose Distribution-Preserving Latent Steganography via Conditional Optimal Transport (DPL-COT), a coverless image steganography framework for latent diffusion models. Unlike classical cover-modifying schemes, DPL-COT embeds a bitstream directly into the initialization noise latent zT∼N(0,I) without model retraining. Our primary objective is high recoverability and a low bit error rate (BER) under deterministic inversion, which is inherently imperfect due to numerical discretization and VAE nonlinearity. To maximize decoding stability, we restrict embedding to the natural tails of the latent prior by selecting the largest-magnitude coordinates, thereby increasing the sign decision margin against inversion drift. To preserve distributional stealth, per-bit target values are analytically derived from truncated Gaussians matching the marginal distribution of the selected coordinates. Conditional 1D optimal transport is applied independently for each bit class, mapping every coordinate to its target value while preserving rank order. We generate 5000 stego images using a pretrained diffusion model and demonstrate a favorable capacity–reliability trade-off (e.g., 4916 bits/image with 0.473% mean BER) and strong robustness to JPEG compression (sub-1% mean BER at Q=60). Compared with LDStega, a recent LDM-based scheme reporting 99.28% clean-channel accuracy, DPL-COT achieves 99.53% at a comparable operating point and sustains above-99% accuracy under all tested JPEG quality factors. Latent-space tests further confirm negligible cover–stego distribution shift (mean KS2<0.003, mean W1<0.003), a property not formally addressed by prior methods.