Bidirectional Centered Score Matching for Discrete Diffusion Distillation
Peng Tu, Baoyou Chen, Haoyuan Xia, Zilong Dong, Weihao Yuan, Siyu Zhu
Abstract
Discrete diffusion models with parallel decoding are often distilled using token-wise KL objectives. Although token-wise KL exactly matches the corresponding product-form block distributions, its probability-space optimization geometry and teacher-only candidate truncation may provide insufficient supervision under aggressive few-step distillation. Concrete Score Matching (CSM) provides an alternative within-position objective by aligning relative logit geometry, but its complete pairwise form incurs $\mathcal{O}(|\mathcal{V}|^2)$ complexity. We propose Bidirectional Centered Score Matching (BCSM), an efficient within-position distillation objective that constructs an $\mathcal{O}(K)$ bidirectional active set, reduces pairwise comparisons to $\mathcal{O}(K^2)$, and factorizes them into an $\mathcal{O}(K)$ objective. We further introduce cross-timestep transition alignment. Experiments demonstrate strong quality--efficiency trade-offs, including up to $6\times$ NFE reduction with a 16.9\% relative HumanEval gain and a 15.1\% relative MMMU gain at single-step inference.