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This paper applies flow matching to unbalanced optimal transport, a method for modeling how cell populations change over time, including birth and death. Its main contribution is making that approach scale to atlas-sized single-cell datasets by exploiting hierarchical annotations and optional lineage priors. Readers working on generative modeling or trajectory inference should note the algorithmic change, but the claims of biologically meaningful results rest on experiments that the abstract alone doesn't let us evaluate.
Multiscale Supervised Unbalanced Optimal Transport Flow Matching
arXiv:2605.16529v2 Announce Type: replace Abstract: Unbalanced optimal transport (UOT) provides a principled framework for modeling single-cell transitions and birth-death dynamics, but its high computational cost limits scalability to large-scale datasets. Although single-cell data often contain hierarchical annotations and known transition priors, existing UOT approximations rarely exploit this multiscale structure or prior knowledge. We introduce Multiscale Supervised Unbalanced Optimal Transport Flow Matching (MUST-FM), a simulation-free framework that scales UOT by leveraging hierarchical data structure. MUST-FM further supports an optional supervised formulation that incorporates transition priors, such as cell lineages, to guide the learning of displacement fields and mass variations. Experiments show that MUST-FM reduces computational overhead while achieving robust and biologically meaningful trajectory inference, enabling dynamic modeling of atlas-scale single-cell datasets. The code is available at https://github.com/QiangweiPeng/MUST-FM.
Abstract:Unbalanced optimal transport (UOT) provides a principled framework for modeling single-cell transitions and birth-death dynamics, but its high computational cost limits scalability to large-scale datasets. Although single-cell data often contain hierarchical annotations and known transition priors, existing UOT approximations rarely exploit this multiscale structure or prior knowledge. We introduce Multiscale Supervised Unbalanced Optimal Transport Flow Matching (MUST-FM), a simulation-free framework that scales UOT by leveraging hierarchical data structure. MUST-FM further supports an optional supervised formulation that incorporates transition priors, such as cell lineages, to guide the learning of displacement fields and mass variations. Experiments show that MUST-FM reduces computational overhead while achieving robust and biologically meaningful trajectory inference, enabling dynamic modeling of atlas-scale single-cell datasets. The code is available at this https URL.
Machine Learning (cs.LG); Optimization and Control (math.OC)
arXiv:2605.16529 [cs.LG]
(or arXiv:2605.16529v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.16529 Focus to learn more arXiv-issued DOI via DataCite
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