Bidirectional Centered Score Matching for Discrete Diffusion Distillation

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.

Artificial Intelligence (cs.AI)

arXiv:2611.04279 [cs.AI]

(or arXiv:2611.04279v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2611.04279 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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