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Advances in machine learning have transformed structural biology, enabling swift and accurate prediction of protein structure from sequence. However, key challenges persist in modeling side-chain packing, condition-dependent conformational changes and biomolecular interactions, largely because of limited high-quality training data. At the same time, emerging experimental techniques such as cryo-electron microscopy (cryo-EM), cryo-electron tomography (cryo-ET) and high-throughput crystallography are generating vast amounts of structural information but converting these data into mechanistically interpretable atomic models often remains difficult. Here we show that integrating experimental measurements directly into protein structure prediction can overcome these limitations. We introduce ROCKET, an augmentation of AlphaFold2 that refines predicted structures using cryo-EM, cryo-ET and X-ray crystallography data. By optimizing structures in the space of coevolutionary embeddings rather than Cartesian coordinates, ROCKET captures biologically meaningful structural variation that is inaccessible to AlphaFold2 alone and to existing automated modeling approaches, especially when the signal-to-noise ratio is low. ROCKET enables scalable, automated model building without retraining and provides a general framework for integrating experimental observables with biomolecular machine learning.