Title: Reconstructing continuous distributions of 3D protein structure from cryo-EM images. Abstract: Cryo-electron microscopy (cryo-EM) is a powerful technique for determining the structure of proteins and other macromolecular complexes at near-atomic resolution. In single particle cryo-EM, the central problem is to reconstruct the 3D structure of a macromolecule from $10^{4-7}$ noisy and randomly oriented 2D projection images. However, the imaged protein complexes may exhibit structural variability, which complicates reconstruction and is typically addressed using discrete clustering approaches that fail to capture the full range of protein dynamics. Here, we introduce a novel method for cryo-EM reconstruction that extends naturally to modeling continuous generative factors of structural heterogeneity. This method encodes structures in Fourier space using coordinate-based deep neural networks, and trains these networks from unlabeled 2D cryo-EM images by combining exact inference over image orientation with variational inference for structural heterogeneity. We demonstrate that the proposed method, termed cryoDRGN, can perform ab-initio reconstruction of 3D protein complexes from simulated and real 2D cryo-EM image data. To our knowledge, cryoDRGN is the first neural network-based approach for cryo-EM reconstruction and the first end-to-end method for directly reconstructing continuous ensembles of protein structures from cryo-EM images.