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Macromolecular structure determination by electron cryo-microscopy (cryo-EM) is limited by the alignment of noisy images of individual particles. Because smaller particles have weaker signals, alignment errors impose size limitations on its applicability. Here, we explore how image alignment is improved by the application of deep learning to exploit prior knowledge about biological macromolecular structures that would otherwise be difficult to express mathematically. We train a denoising convolutional neural network on pairs of half-set reconstructions from the electron microscopy data bank (EMDB) and use this denoiser as an alternative to a commonly used smoothness prior. We demonstrate that this approach, which we call Blush regularization, yields better reconstructions than do existing algorithms, in particular for data with low signal-to-noise ratios. The reconstruction of a protein-nucleic acid complex with a molecular weight of 40 kDa, which was previously intractable, illustrates that denoising neural networks will expand the applicability of cryo-EM structure determination for a wide range of biological macromolecules.