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Although single-cell and spatial sequencing methods enable simultaneous measurement of more than one biological modality, no technology can capture all modalities within the same cell. For current data integration methods, the feasibility of cross-modal integration relies on the existence of highly correlated, a priori ‘linked’ features. We describe matching X-modality via fuzzy smoothed embedding (MaxFuse), a cross-modal data integration method that, through iterative coembedding, data smoothing and cell matching, uses all information in each modality to obtain high-quality integration even when features are weakly linked. MaxFuse is modality-agnostic and demonstrates high robustness and accuracy in the weak linkage scenario, achieving 20~70% relative improvement over existing methods under key evaluation metrics on benchmarking datasets. A prototypical example of weak linkage is the integration …