Flow Duality and Source Geometry for Categorical Generation
Continuous and discrete flow matching are usually treated as separate constructions. This paper identifies a duality between them: projecting continuous convex-interpolant flows with one-hot targets through a position-wise argmax yields discrete convex-interpolant flows. The result requires source laws with appropriate coordinate symmetry and regularity, and it makes the continuous source distribution an explicit design choice for categorical generation. We derive the induced discrete interpolation behavior for Gaussian, bounded-uniform, and centered negative-exponential sources, showing that different source geometries lead to qualitatively different transition timing and vocabulary-size...
| Authors | Etrit Haxholli |
|---|---|
| Primary category | cs.LG |
| Published | 9 September 2026 |
| Last updated at source | 13 September 2026 |
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