Tessellations of Semi-Discrete Flow Matching

ArXi:2605.07513v1 Announce Type: new We study Flow Matching in a semi-discrete setting where a Gaussian source is transported toward a discrete target ed on finitely many points. This semi-discrete regime is the theoretical setting behind the use of Flow Matching for generative modeling, where the target distribution is represented by a finite dataset. In this semi-discrete regime, the exact Flow Matching velocity field is available in closed form, which makes it possible to analyze the geometry induced by the terminal flow map independently of optimization and approximation effects.