SOURCE-LINKED INTELLIGENCE

Flow Duality and Source Geometry for Categorical Generation

arXiv · AI, language, vision and robotics · article · Sep 9, 2026 · UTC

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

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