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Federated ensemble distillation addresses client heterogeneity by generating pseudo-labels for an unlabeled server dataset based on client predictions and training the server model using the pseudo-labeled dataset. The unlabeled server dataset can either be pre-existing or generated through a data-free approach. The effectiveness of this approach critically depends on the method of assigning weights to client predictions when creating pseudo-labels, especially in highly heterogeneous settings. Inspired by theoretical results from GANs, we propose a provably near-optimal weighting method that leverages client discriminators trained with a server-distributed generator and local datasets. Our experiments on various image classification tasks demonstrate that the proposed method significantly outperforms baselines. Furthermore, we show that the additional communication cost, client-side privacy leakage, and client-side computational overhead introduced by our method are negligible, both in scenarios with and without a pre-existing server dataset.