Categorical Flow Matching via Simplex-to-Euclidean Bijections

We propose a simple framework for learning and sampling from probability distributions supported on the simplex. Our approach maps the open simplex to the Euclidean space via smooth bijections, so we can model the density in the Euclidean space. This density is linked to categorical observations via a Dirichlet interpolation. Compared to previous methods that operate on the simplex using Riemannian geometry or custom noise processes, our approach is simpler while achieving competitive performance on both synthetic and real-world datasets.