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arXiv · 2602.12233

Categorical Flow Maps

Daan Roos·Oscar Davis·Floor Eijkelboom·Michael Bronstein·Max Welling·İsmail İlkan Ceylan·Luca Ambrogioni·Jan-Willem van de Meent
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Abstract

We introduce Categorical Flow Maps, a flow-matching method for accelerated few-step generation of categorical data via self-distillation. Building on recent variational formulations of flow matching and the broader trend towards accelerated inference in diffusion and flow-based models, we define a flow map towards the simplex that transports probability mass toward a predicted endpoint, yielding a parametrisation that naturally constrains model predictions. Since our trajectories are continuous rather than discrete, Categorical Flow Maps can be trained with existing distillation techniques, as well as a new objective based on endpoint consistency. This continuous formulation also automatically unlocks test-time inference: we can directly reuse existing guidance and reweighting techniques in the categorical setting to steer sampling toward downstream objectives. Empirically, we achieve state-of-the-art few-step results on images, molecular graphs, and text, with strong performance even in single-step generation.

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Daan Roos, Oscar Davis, Floor Eijkelboom, Michael Bronstein, Max Welling, İsmail İlkan Ceylan, Luca Ambrogioni, Jan-Willem van de Meent. 2026-02-12. Categorical Flow Maps. https://arxiv.org/abs/2602.12233

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