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About this paper
Emile Pierret, Johannes Hertrich, Samuel Hurault, Julie Delon
The authors analyze exact flow-matching assignment cells for a standard Gaussian source and a finite set of targets. A closed-form velocity averages drifts toward targets using endpoint weights. Every cell is open and simply connected, yet a proved four-atom example differs from Laguerre cells in convexity, boundedness, boundary shape, and adjacency. These claims concern exact flows, not trained models.
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