Federated learning (FL) effectively mitigates the data silo challenge brought about by policies and privacy concerns, implicitly harnessing more data for deep model training. However, traditional centralized FL models grapple with diverse multi-center data, especially in the face of significant data heterogeneity, notably in medical contexts. In the realm of medical image segmentation, the growing imperative to curtail annotation costs has amplified the importance of weakly-supervised techniques which utilize sparse annotations such as points, scribbles, etc. A pragmatic FL paradigm shall accommodate diverse annotation formats across different sites, which research topic remains under-investigated. In such context, we propose a novel personalized FL framework with learnable prompt and aggregation (FedLPPA) to uniformly leverage heterogeneous weak supervision for medical image segmentation. In FedLPPA, a learnable universal knowledge prompt is maintained, complemented by multiple learnable personalized data distribution prompts and prompts representing the supervision sparsity. Integrated with sample features through a dual-attention mechanism, those prompts empower each local task decoder to adeptly adjust to both the local distribution and the supervision form. Concurrently, a dual-decoder strategy, predicated on prompt similarity, is introduced for enhancing the generation of pseudo-labels in weakly-supervised learning, alleviating overfitting and noise accumulation inherent to local data, while an adaptable aggregation method is employed to customize the task decoder on a parameter-wise basis. Extensive experiments on four distinct medical image segmentation tasks involving different modalities underscore the superiority of FedLPPA, with its efficacy closely parallels that of fully supervised centralized training. Our code and data will be available.

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