Structured Coupling for Flow Matching

2026-05-08

AI Summary

This work addresses the limitations of existing flow matching methods, which lack interpretable latent structure, and conventional latent variable models, which often compromise generation quality for structural expressiveness. To bridge this gap, the paper proposes Structured Coupled Flow Matching (SCFM), which uniquely integrates structured latent variables into the flow matching framework. SCFM jointly learns a structured prior and a continuous transport map by introducing structured latent variables alongside exogenous noise in the source distribution. A shared time-dependent inference network enables simultaneous variational inference and estimation of flow velocities at intermediate time steps. Experiments demonstrate that SCFM achieves generation quality on par with standard flow matching while significantly enhancing unsupervised representation learning, thereby effectively supporting downstream tasks such as clustering and disentanglement.

Abstract

Standard flow matching scales well but typically relies on an unstructured source distribution, limiting its ability to learn interpretable latent structure. Latent-variable models, by contrast, capture structure but often sacrifice generative quality. We bridge this gap by proposing Structured Coupling for Flow Matching (SCFM), a cooperative framework that augments flow matching with structured latent representation learning. By introducing structured latent variables and exogenous noise into the source, SCFM jointly learns a structured prior (via latent variable modeling) and a continuous transport map (via flow matching). It uses a shared time-dependent recognition network for both latent variable model variational inference and intermediate-time flow velocity estimation. This yields a structurally informed yet unconditional, simulation-free flow model, where the latent variable model can also assist flow sampling. Empirically, SCFM facilitates unsupervised latent representation learning for clustering, disentanglement and downstream tasks, while remaining competitive with flow matching in sample quality, showing that meaningful structure can be learned without sacrificing generative fidelity.

Problem

• flow matching
• structured latent representation
• generative modeling
• latent variable models
• unsupervised representation learning

Innovation

• Structured Coupling
• Flow Matching
• Latent Variable Modeling
• Continuous Transport
• Unsupervised Representation Learning