Multiscale Supervised Unbalanced Optimal Transport Flow Matching

2026-05-15

AI Summary

This work addresses the computational inefficiency and limited scalability of unbalanced optimal transport (UOT) in large-scale single-cell data analysis, as well as its neglect of multiscale structures and biological priors. To overcome these limitations, we propose MUST-FM, a novel framework that integrates hierarchical data organization and biological prior knowledge—such as cell lineage—into UOT-based flow matching. MUST-FM enables efficient learning of displacement fields and mass changes without requiring simulation, leveraging multiscale modeling and supervised guidance. This approach substantially reduces computational overhead while achieving scalable, robust, and biologically plausible inference of dynamic cellular trajectories across large single-cell atlases.

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.

Problem

• unbalanced optimal transport
• single-cell data
• multiscale structure
• transition priors
• computational scalability

Innovation

• Unbalanced Optimal Transport
• Multiscale Structure
• Supervised Learning
• Single-cell Trajectory Inference
• Flow Matching