CoDMD: Copula-aware Distribution Matching Distillation for Fast Video Generation

Few-step distillation for video diffusion models has attracted significant attention, driven by the urgent demand for efficient deployment in real-world scenarios. However, Distribution Matching Distillation (DMD), a leading paradigm, tends to degrade under limited NFE budgets, manifesting in video generation as layout instability, oversaturation, and broken motion dynamics. We trace this failure to a structural limitation: standard DMD is an intra-sample distribution-matching objective with coordinate-wise gradients, and thus imposes no explicit constraint on the relational geometry across batch elements or temporal frames, leaving the underlying copula largely unregulated. Combined with the mode-seeking tendency of its reverse-KL objective, this absence of relational guidance makes DMD prone to collapsing into local optima in the few-step regime. Motivated by this insight, we propose Copula-aware DMD (CoDMD), a lightweight relational regularizer that reuses score estimates already produced by the frozen teacher and the online fake model to construct pairwise relation matrices across samples and frames.These are matched through a supplementary distributional objective that requires no additional networks, datasets, or sampling trajectories. On the Wan-2.1-T2V model series at 1.3B \& 14B scales, CoDMD distills 50-step teachers into 4-step students, achieving an approximate 25$\times$ speed-up while attaining VBench scores of 84.46 \& 84.87, outperforming prior trajectory-based (rCM 82.81 \& 84.05) and distribution-based (DMD 83.38 \& 83.81) methods.