Federated learning (FL) enables collaborative training of medical image segmentation models without sharing raw patient data, yet existing approaches assume a homogeneous compute budget across institutions, limiting participation of low-resource sites. We propose Fed-ADApt, a depth-adaptive federated framework for UNet-based segmentation that jointly addresses low-compute training and inference. Fed-ADApt integrates multi-depth supervision with hierarchical depth-wise aggregation, allowing each site to train according to its local compute budget while contributing to a global model that supports dynamic depth selection at deployment. We evaluated Fed-ADApt on multi-site 2D retinal fundus disc segmentation and 3D brain tumor segmentation. Across both tasks, federated collaboration substantially improves robustness under domain shift. Fed-ADApt matched the full-resource FedAvg performance in 3D and achieved competitive 2D performance with a 4.7% average Dice reduction, while reducing average inference cost by 19.5% in 3D and 34.5% in 2D and substantially reducing training cost by 98% at the most constrained sites. Importantly, Fed-ADApt enables low-resource institutions that cannot train full-capacity models to participate in federations while maintaining competitive global performance under a favorable accuracy to efficiency trade-off. By considering training and inference compute budgets, Fed-ADApt provides a practical and equitable solution for federated medical image segmentation across heterogeneous clinical and edge-enabled imaging environments.

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