Training of multimodal foundation models is currently restricted to centralized data centers containing massive, aligned datasets (e.g., image-text pairs). However, in realistic federated environments, data is often unpaired and fragmented across disjoint nodes; one node may hold sensor data, while another holds textual logs. These datasets are strictly private and share no common samples. Current federated learning (FL) methods fail in this regime, as they assume local clients possess aligned pairs or require sharing raw feature embeddings, which violates data sovereignty. We propose a novel framework to train a global multimodal transformer across decentralized nodes with disjoint modalities. We introduce a small public anchor set to align disjoint private manifolds. Using Gram matrices calculated from these public anchors, we enforce semantic alignment across modalities through centered kernel alignment without ever transmitting private samples, offering a mathematically superior privacy guarantee compared to prototype sharing. Further, we introduce a subspace-stabilized fine-tuning method to handle FL with huge transformer models. We strictly decouple domain-specific magnitude shifts from semantic direction, ensuring that nodes with varying sensor characteristics align geometrically to the global consensus. Lastly, we propose precision weighted averaging, where efficiently obtained uncertainty estimates are used to downweight uncertain nodes. This paper establishes the mathematical backbone for federated unpaired foundation models, enabling a global model to learn a unified representation of the world from fragmented, disjoint, and private data silos without requiring centralized storage or paired samples.

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