Categorical Flow Maps

Daan Roos, Oscar Davis, Floor Eijkelboom, Michael M. Bronstein, Max Welling, İsmail İlkan Ceylan, Luca Ambrogioni, Jan-Willem Van De Meent
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:105618-105642, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-roos26a, title = {Categorical Flow Maps}, author = {Roos, Daan and Davis, Oscar and Eijkelboom, Floor and Bronstein, Michael M. and Welling, Max and Ceylan, \.{I}smail \.{I}lkan and Ambrogioni, Luca and Van De Meent, Jan-Willem}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {105618--105642}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/roos26a/roos26a.pdf}, url = {https://proceedings.mlr.press/v306/roos26a.html}, 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.} }
Endnote
%0 Conference Paper %T Categorical Flow Maps %A Daan Roos %A Oscar Davis %A Floor Eijkelboom %A Michael M. Bronstein %A Max Welling %A İsmail İlkan Ceylan %A Luca Ambrogioni %A Jan-Willem Van De Meent %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-roos26a %I PMLR %P 105618--105642 %U https://proceedings.mlr.press/v306/roos26a.html %V 306 %X 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.
APA
Roos, D., Davis, O., Eijkelboom, F., Bronstein, M.M., Welling, M., Ceylan, İ.İ., Ambrogioni, L. & Van De Meent, J.. (2026). Categorical Flow Maps. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:105618-105642 Available from https://proceedings.mlr.press/v306/roos26a.html.

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