Large single-cell atlases are now routinely generated to serve as references for analysis of smaller-scale studies. Yet learning from reference data is complicated by batch effects between datasets, limited availability of computational resources and sharing restrictions on raw data. Here we introduce a deep learning strategy for mapping query datasets on top of a reference called single-cell architectural surgery (scArches). scArches uses transfer learning and parameter optimization to enable efficient, decentralized, iterative reference building and contextualization of new datasets with existing references without sharing raw data. Using examples from mouse brain, pancreas, immune and whole-organism atlases, we show that scArches preserves biological state information while removing batch effects, despite using four orders of magnitude fewer parameters than de novo integration. scArches generalizes to multimodal reference mapping, allowing imputation of missing modalities. Finally, scArches retains coronavirus disease 2019 (COVID-19) disease variation when mapping to a healthy reference, enabling the discovery of disease-specific cell states. scArches will facilitate collaborative projects by enabling iterative construction, updating, sharing and efficient use of reference atlases.