We introduce Coupled Flow Matching (CPFM), a framework that integrates controllable dimensionality reduction and high-fidelity reconstruction. CPFM learns coupled continuous flows for both the high-dimensional data x and the low-dimensional embedding y, which enables sampling p(y|x) via a latent-space flow and p(x|y) via a data-space flow. Unlike classical dimension-reduction methods, where information discarded during compression is often difficult to recover, CPFM preserves the knowledge of residual information within the weights of a flow network. This design provides bespoke controllability: users may decide which semantic factors to retain explicitly in the latent space, while the complementary information remains recoverable through the flow network. Coupled flow matching builds on two components: (i) an extended Gromov-Wasserstein optimal transport objective that establishes a probabilistic correspondence between data and embeddings, and (ii) a dual-conditional flow-matching network that extrapolates the correspondence to the underlying space. Experiments on multiple benchmarks show that CPFM yields semantically rich embeddings and reconstructs data with higher fidelity than existing baselines.

翻译：我们提出了耦合流匹配（CPFM）框架，该框架集成了可控降维与高保真重建功能。CPFM同时学习高维数据x与低维嵌入y的耦合连续流，从而能够通过潜在空间流采样p(y|x)并通过数据空间流采样p(x|y)。与经典降维方法在压缩过程中丢弃的信息通常难以恢复不同，CPFM将残差信息的知识保存在流网络的权重中。该设计提供了定制化的可控性：用户可自主决定在潜在空间中显式保留哪些语义因子，而互补信息仍可通过流网络进行恢复。耦合流匹配建立在两个核心组件之上：(i) 扩展的Gromov-Wasserstein最优传输目标，用于建立数据与嵌入之间的概率对应关系；(ii) 双条件流匹配网络，将该对应关系外推至底层空间。在多个基准测试上的实验表明，CPFM能生成语义丰富的嵌入表示，并相比现有基线方法实现更高保真度的数据重建。