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Extracting predictive features from high-dimensional multimodal inputs is particularly challenging in this setting: data cannot leave each client, local samples are scarce and heterogeneously distributed, and unsupervised dimensionality reduction discards task-relevant information while federated training introduces representation drift across communication rounds. FDRMFL addresses these challenges through a unified four-term local objective: MSE prediction loss, a correlation-based mutual information surrogate that preserves dependence between the fused representation and the continuous target, a symmetric KL penalty that aligns cross-modal latent distributions before fusion, and an InfoNCE-style contrastive loss that anchors local representations to the global consensus. 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FDRMFL addresses these challenges through a unified four-term local objective: MSE prediction loss, a correlation-based mutual information surrogate that preserves dependence between the fused representation and the continuous target, a symmetric KL penalty that aligns cross-modal latent distributions before fusion, and an InfoNCE-style contrastive loss that anchors local representations to the global consensus. 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