Guidance Without Labels: Flow Matching from Coupled Gaussian Mixtures
Flow matching models are typically trained to transport a Gaussian source to the data distribution, with source and target samples paired independently. We replace the source with a fitted Gaussian mixture and couple each data point to a mixture component through an entropic optimal transport problem. We show that the resulting transport reduces to the standard Gaussian-source problem up to a guidance-like correction, which enables the reuse of a pretrained velocity field. This correction is a closed-form function of the fitted mixture plus a term that we learn with a small correction network. We test our model on published checkpoints for CIFAR-10 and CelebA-HQ. It improves FID at every ...
| Authors | Stanislas Ducotterd, Bassam El Rawas, Michael Unser |
|---|---|
| Primary category | cs.LG |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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