Coupled Flow Matching

TL;DR

Coupled Flow Matching (CPFM) introduces a novel framework that combines controllable dimensionality reduction with high-fidelity data reconstruction, leveraging coupled flows and optimal transport to preserve residual information and enable semantic control.

Contribution

CPFM is the first to integrate coupled flow models with optimal transport for controllable, high-fidelity data embedding and reconstruction, surpassing existing dimension reduction methods.

Findings

CPFM produces semantically rich embeddings.

CPFM achieves higher reconstruction fidelity than baselines.

CPFM enables explicit control over retained semantic factors.

Abstract

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.