COT-FM：基于聚类最优传输的流匹配方法

摘要

我们提出COT-FM这一通用框架，通过重构流匹配（FM）中的概率路径来实现更快速、更可靠的生成。传统FM模型由于采用随机或批量耦合方式，往往产生弯曲的轨迹路径，这会增加离散化误差并降低样本质量。COT-FM通过聚类目标样本，并为每个聚类分配通过逆向预训练FM模型获得的专用源分布，从而有效解决这一问题。这种分治策略在不改变模型架构的前提下，实现了更精确的局部传输和显著平直化的向量场。作为即插即用方案，COT-FM在二维数据集、图像生成基准测试以及机器人操作任务中，持续加速采样过程并提升生成质量。

English

We introduce COT-FM, a general framework that reshapes the probability path in Flow Matching (FM) to achieve faster and more reliable generation. FM models often produce curved trajectories due to random or batchwise couplings, which increase discretization error and reduce sample quality. COT-FM fixes this by clustering target samples and assigning each cluster a dedicated source distribution obtained by reversing pretrained FM models. This divide-and-conquer strategy yields more accurate local transport and significantly straighter vector fields, all without changing the model architecture. As a plug-and-play approach, COT-FM consistently accelerates sampling and improves generation quality across 2D datasets, image generation benchmarks, and robotic manipulation tasks.

COT-FM：基于聚类最优传输的流匹配方法

COT-FM: Cluster-wise Optimal Transport Flow Matching

摘要

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