Tessellations of Semi-Discrete Flow Matching
We study Flow Matching in a semi-discrete setting where a Gaussian source is transported toward a discrete target supported 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. We investigate the terminal assignment regions, namely the preimages of the target atoms under the terminal flow. We show that these reg...
| Authors | Emile Pierret, Johannes Hertrich, Samuel Hurault et al. |
|---|---|
| Primary category | cs.LG |
| Published | 8 May 2026 |
| Last updated at source | 8 May 2026 |
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