提出新型耦合结构,让生成模型路径不交叉且训练更快。
Beyond Straightness: Non-Crossing Flow Matching via Quantile AlignTree Coupling

- 用分位数对齐的树结构构建数据与先验的分层耦合
- 路径不交叉,中间时刻分离度更高,速度歧义减少
- 支持条件生成,大规模高维任务训练效率显著提升
流匹配性能高度依赖源分布与目标分布间的耦合质量。独立耦合常导致路径交叉和局部速度歧义,而基于最优传输(OT)的耦合则构造成本过高。为此,我们提出分位数对齐树流匹配(QAT-FM),一种高效的结构化耦合策略,通过分位数对齐的树结构在高斯先验与目标数据分布间构建分层耦合。QAT-FM 的构造复杂度为 $\mathcal{O}(Nd\log N)$,支持每对样本的源采样复杂度为 $\mathcal{O}(d)$,适用于大规模高维生成任务的可扩展训练。理论上,我们证明该耦合满足边际一致性,诱导非交叉线性插值路径,并在中间时刻持续改善路径分离度,缓解局部速度歧义。QAT-FM 可自然推广至条件生成,实现结构化条件耦合同时保持全局高斯对齐。在多种基准数据集上的实验表明,QAT-FM 在生成性能上具有竞争力,同时大幅降低耦合构造成本。
原文摘要 · Abstract (English)
The performance of Flow Matching largely depends on the quality of the coupling between the source and target distributions. However, independent coupling often leads to path crossings and local velocity ambiguity, while OT-based couplings typically incur high construction costs. To address this challenge, we propose Quantile AlignTree Flow Matching (QAT-FM), an efficient structured coupling strategy that constructs a hierarchical coupling between a Gaussian prior and the target data distribution via a quantile-aligned tree structure. QAT-FM constructs the coupling in $\mathcal{O}(Nd\log N)$ time and supports per-pair source sampling with $\mathcal{O}(d)$ complexity, enabling scalable training for large-scale high-dimensional generative tasks. Theoretically, we prove that the QAT coupling satisfies marginal consistency, induces non-crossing linear interpolation paths, and consistently improves path separation at intermediate times compared with independent coupling, thereby alleviating local velocity ambiguity. QAT-FM further extends naturally to conditional generation, enabling structured conditional coupling while preserving global Gaussian alignment. Experiments across diverse benchmark datasets demonstrate that QAT-FM achieves competitive generative performance while substantially reducing coupling construction cost.
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