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We introduce blueprint separable convolutions (BSConv) as highly efficient building blocks for CNNs. They are motivated by quantitative analyses of kernel properties from trained models, which show the dominance of correlations along the depth axis. Based on our findings, we formulate a theoretical foundation from which we derive efficient implementations using only standard layers. Moreover, our approach provides a thorough theoretical derivation, interpretation, and justification for the application of depthwise separable convolutions (DSCs) in general, which have become the basis of many modern network architectures. Ultimately, we reveal that DSC-based architectures such as MobileNets implicitly rely on cross-kernel correlations, while our BSConv formulation is based on intra-kernel correlations and thus allows for a more efficient separation of regular convolutions. Extensive experiments on large-scale and fine-grained classification datasets show that BSConvs clearly and consistently improve MobileNets and other DSC-based architectures without introducing any further complexity. For fine-grained datasets, we achieve an improvement of up to 13.7 percentage points. In addition, if used as drop-in replacement for standard architectures such as ResNets, BSConv variants also outperform their vanilla counterparts by up to 9.5 percentage points on ImageNet. Code and models are available under https://github.com/zeiss-microscopy/BSConv.