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TITLE: Reweighted Flow Matching via Unbalanced OT for Label-free Long-tailed Generation

ABSTRACT: Flow matching has recently emerged as a powerful framework for continuous-time generative modeling. However, when applied to long-tailed distributions, standard flow matching suffers from majority bias, producing minority modes with low fidelity and failing to match the true class proportions. In this work, we propose Unbalanced Optimal Transport Reweighted Flow Matching (UOT-RFM), a novel framework for generative modeling under class-imbalanced (long-tailed) distributions that operates without any class label information. Our method constructs the conditional vector field using mini-batch Unbalanced Optimal Transport (UOT) and mitigates majority bias through a principled inverse reweighting strategy. The reweighting relies on a label-free majority score, defined as the density ratio between the target distribution and the UOT marginal. This score quantifies the degree of majority based on the geometric structure of the data, without requiring class labels. By incorporating this score into the training objective, UOT-RFM theoretically recovers the target distribution with first-order correction (k = 1) and empirically improves tail-class generation through higher-order corrections (k > 1). Our model outperforms existing flow matching baselines on long-tailed benchmarks, while maintaining competitive performance on balanced datasets.