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Structured Coupling for Flow Matching

NeurIPS 2026 · Probabilistic and scientific modeling › Variational and generative sampling · approach: Expressive invertible architectures · 0 citations (OpenAlex)

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Proposes SCFM, which augments flow matching with a learnable structured GMM latent source x0=(z,ε) trained jointly with a VAE-style endpoint objective via a shared time-dependent recognition network, yielding structured latents while matching FM sample quality.

Problem

Standard flow matching uses an unstructured fixed source distribution, so its learned transport does not expose interpretable latent structure, while latent-variable models that learn structure often have weak generative quality.

Approach

Makes the flow source structured and learnable by augmenting it as x0=(z,ε), where z is a GMM-prior latent inferred by an encoder-induced coupling from data; a single time-dependent recognition network serves as VAE encoder at t=1 and as variational posterior mean for flow velocity at t<1, plus optional decoder-initialized refinement sampling.

Key results

• CIFAR-10 FID 2.117 for SCFM vs 2.137 for flow matching; ImageNet-128 FID 17.180 (unconditional) vs 17.243 for class-conditional SiT-XL/2.
• MNIST clustering: best SCFM variant improves NMI by nearly 8 points and ACC by more than 13 points over VaDE.
• ImageNet-128 nonlinear probe Top-1 rises from 12.34 (SD-VAE) to 27.96 for SCFM.

Surprising findings

• Unconditional SCFM on ImageNet-128 slightly outperforms class-conditional SiT-XL/2 in FID.

Limitations

• Roughly 1.5-2.4x training/inference FLOP and parameter overhead versus standard flow matching.
• Decoder-based sampling depends on endpoint VAE quality; posterior collapse degrades refinement.
• Prior-aggregated-posterior matching is only a tractable regularizer, not guaranteed exact alignment.

Experimental setup

Datasets: MNIST Cars3D Shapes3D CIFAR-10 ImageNet-128

Benchmarks: MNIST clustering (NMI, ACC) Cars3D disentanglement Shapes3D disentanglement CIFAR-10 FID 50K CIFAR-10 latent probing ImageNet-128 FID 50K ImageNet-128 latent probing

Metrics: NMI ACC FactorVAE score DCI FID linear probe accuracy nonlinear probe accuracy Top-1 Top-5

Baselines: VaDE MFCVAE VAE AAE BiGAN DIM SD-VAE DisDiff FDAE EncDiff DyGA Flow Matching

Builds on: variational flow matching stochastic interpolants beta-VAE beta-TCVAE VAE

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