Candidate-specific Context Coupling for Discrete Diffusion Preference Optimization

Preference optimization aligns discrete diffusion models with sequence-level rewards through predictions on partially masked candidates. Existing approaches improve preference objectives and denoising estimates, but uniform masking treats all eligible positions alike. With candidate-specific contexts, the joint sampling of conditional scores also shapes the nonlinear preference objective. We introduce Candidate-specific Context Coupling (${\text{C}}^3$), which coordinates reveal progress, counts, and orders while preserving each candidate's selected context distribution. Low-confidence-first supplies a one-pass selector. For fixed Plackett–Luce reveal laws, shared Gumbels simultaneously minimize expected Kendall disagreement on common positions. Under score-response conditions, they also minimize a derived preference-discrepancy upper bound at a fixed joint distribution of shared progress and reveal counts. The method supports pairwise and listwise losses and requires one additional confidence evaluation per candidate. Experiments show gains across DNA sequence design, protein inverse folding, and language modeling, including a 17% relative gain over the strongest baseline in protein inverse folding. Our anonymous code is available at https://anonymous.4open.science/r/C3-C9D7/.