Beyond Local Prediction Frequencies: Hidden Path Coupling in Masked Diffusion

Masked diffusion language models (MDLMs) are trained through local masked predictions, but generation composes these predictions along complete reveal schedules. A broad class of training objectives and train–inference alignment methods depends on a schedule only through how often each local prediction problem is used, so frequency-matched schedules induce the same training objective. We prove that this training equivalence does not imply generation equivalence: schedules with the same objective can still produce different output distributions. We characterize exactly what information this frequency-based view loses and how the missing structure changes generation, and further prove that training generically becomes sensitive to it in our shared-representation population model; a controlled Transformer shows the same effect under symmetric masking. Near mutually consistent local predictions, we also identify the minimal additional schedule information whose matching removes every second-order discrepancy and derive a likelihood-based test requiring no retraining. On MDLM-OWT, output distributions differ by a median $43\%$ in total variation across randomly sampled schedule pairs with identical local prediction frequencies.