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The approach uses measure transport by randomized assignment flows on the statistical submanifold of factorizing distributions, which enables to represent and sample efficiently from any target distribution and to assess the likelihood of unseen data points. The complexity of the target distribution only depends on the parametrization of the affinity function of the dynamical assignment flow system. Our model can be trained in a simulation-free manner by conditional Riemannian flow matching, using the training data encoded as geodesics on the assignment manifold in a closed form, with respect to the e-connection of information geometry. Numerical experiments devoted to distributions of structured image labelings demonstrate the applicability to large-scale problems, which may include discrete distributions in other application areas. Performance measures show that our approach scales better with the increasing number of classes than the recent related work.<\/jats:p>","DOI":"10.1007\/s10851-025-01239-9","type":"journal-article","created":{"date-parts":[[2025,5,28]],"date-time":"2025-05-28T10:49:06Z","timestamp":1748429346000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Generative Assignment Flows for Representing and Learning Joint Distributions of Discrete Data"],"prefix":"10.1007","volume":"67","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3490-3350","authenticated-orcid":false,"given":"Bastian","family":"Boll","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4636-3697","authenticated-orcid":false,"given":"Daniel","family":"Gonzalez-Alvarado","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7189-2275","authenticated-orcid":false,"given":"Stefania","family":"Petra","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8999-2338","authenticated-orcid":false,"given":"Christoph","family":"Schn\u00f6rr","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,28]]},"reference":[{"key":"1239_CR1","volume-title":"Categorial Data Analysis","author":"A Agresti","year":"2013","unstructured":"Agresti, A.: Categorial Data Analysis, 3rd edn. 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