TE-CSA: trajectory entropy-aware cross-step aggregation for improving embedding capacity of distribution-preserving linguistic steganography

Abstract Existing diffusion-based linguistic steganography methods largely operate in a timestep-local manner, where embedding decisions are made independently within isolated denoising steps. Such a design fundamentally underutilizes the trajectory-level uncertainty naturally distributed across the diffusion process, causing a substantial gap between achievable embedding performance and the embedding opportunities available throughout the diffusion trajectory. In this paper, we propose TE-CSA, a Trajectory Entropy-aware Cross-Step Aggregation framework for high-capacity distribution-preserving linguistic steganography based on diffusion language models. First, departing from conventional timestep-local embedding paradigms, TE-CSA introduces a trajectory-level aggregation mechanism that jointly exploits embedding opportunities scattered across multiple denoising timesteps. By transforming isolated local candidates into globally coordinated embedding resources, the proposed framework significantly enlarges the effective embedding space and unlocks latent capacity hidden within diffusion trajectories. Second, from an information-theoretic perspective, not all candidate positions contribute equally to embedding. Low-entropy positions often behave as bottlenecks that consume embedding opportunities while providing little effective information gain. To alleviate this entropy bottleneck, TE-CSA incorporates an entropy-aware filtering strategy that selectively retains informative candidate positions and allocates embedding operations to regions with higher entropy concentration, thereby improving effective embedding utilization and enhancing the capacity–quality trade-off. Finally, a distribution-preserving probabilistic sampling mechanism is employed to keep embedding statistically consistent with the original diffusion generation process. Under the assumption that the underlying probabilistic embedding procedure preserves the target token distribution, cross-step aggregation and entropy-aware filtering do not alter the sampling probabilities themselves, thereby retaining the distribution-preserving security property while maintaining natural text quality. We further derive a group-constrained trajectory-level capacity bound for the adopted three-position redundant embedding mechanism and show that capacity-sorted grouping attains this bound under complete trajectory availability. Experimental results demonstrate that TE-CSA achieves up to 18.60 $$\times$$ × higher embedding capacity and 20.40 $$\times$$ × higher embedding rate (from 0.09 to 1.84 bits/token) than the architecture-matched timestep-local diffusion baseline, while maintaining limited runtime overhead and generation-quality degradation.