Coupled Flow Matching

2025-10-27

AI Summary

Traditional dimensionality reduction methods irreversibly discard semantic information during compression, struggling to balance controllability and reconstruction fidelity. This paper proposes Coupled Flow Matching (CPFM), a bidirectional differentiable dimensionality transformation framework that jointly models continuous probability flows over high-dimensional data $x$ and low-dimensional embeddings $y$. Its core contributions are: (1) an extended Gromov–Wasserstein optimal transport formulation that enforces structural preservation via probabilistic alignment between data and latent spaces; and (2) a dual-conditional flow matching network that generalizes sparse correspondences to the full space—explicitly preserving user-specified semantic factors while implicitly encoding residual information for high-fidelity reconstruction. Experiments demonstrate that CPFM significantly outperforms state-of-the-art dimensionality reduction and generative models in semantic disentanglement, reconstruction quality, and downstream task performance.

Technology Category

• Machine Learning: Dimensionality Reduction/Feature Selection
• Computer Vision: Diffusion Models for Vision
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• CPFM integrates controllable dimensionality reduction with high-fidelity reconstruction
• It preserves residual information within flow network weights during compression
• Enables explicit semantic factor control in latent space while recovering complementary data

Innovation

• Coupled continuous flows for data and embeddings
• Preserves residual information in flow network weights
• Uses Gromov-Wasserstein transport and dual-conditional network