Bridging the Gap Between Plausibility and Admissibility: Constraint-Aware Flow Maps for Dynamic Graph Systems

Generative models can support decision-making under uncertainty by producing ensembles of plausible future system trajectories, but statistical plausibility does not ensure structural feasibility. This study investigates whether post-sampling symbolic constraints can improve the reliability of generative trajectory modeling in dynamic graph-structured systems. A conditional diffusion model generates future graph-state trajectories from partial observations, while an external symbolic layer applies hard filtering, soft weighting, or projection-based repair. The framework is evaluated on two controlled synthetic regimes: a compact graph and a medium-complexity dependency graph, using metrics for structural validity, sample efficiency, diversity, robustness, and calibration. In the compact regime, the model produces an invalid probability mass of 0.002996, indicating an almost entirely admissible trajectory manifold. Under the same architecture and training protocol, invalid mass increases to 0.155929 in the medium-complexity regime. Hard filtering removes all invalid retained trajectories while preserving 84.4% of generated samples, whereas soft weighting preserves effective sample size but yields only limited validity gains. Family-level analysis shows that dependency constraints account for nearly all observed inadmissibility. These results indicate that statistical plausibility and structural admissibility are distinct reliability properties and that symbolic constraint handling becomes more valuable as graph-structural complexity increases.