Structured Coupling for Flow Matching

TL;DR

SCFM introduces a structured latent variable approach to flow matching, enabling interpretable representations without compromising sample quality, thus bridging the gap between structure learning and generative performance.

Contribution

It proposes a novel framework that integrates structured latent variables into flow matching, enhancing interpretability and downstream task performance while maintaining high sample quality.

Findings

Enables unsupervised latent representation learning for clustering and disentanglement.

Maintains competitive sample quality compared to traditional flow matching.

Facilitates structure learning without sacrificing generative fidelity.

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.