Paper:
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 networkbased approach for cryo-EM reconstruction and the first end-to-end method for directly reconstructing continuous ensembles of protein structures from cryo-EM images.

Review:
~The authors build a new method to recapitulate the 3D structure of a biomolecule from cryo-EM images that allows for flexibility in the reconstructed volume.~
I thought this paper is very well written and tackles a difficult project. 
There is a previous work that these authors should cite:
Ullrich, K., Berg, R.V.D., Brubaker, M., Fleet, D. and Welling, M., 2019. Differentiable probabilistic models of scientific imaging with the Fourier slice theorem. arXiv preprint arXiv:1906.07582.
How does your method compare to this paper? In Ullrich et al., they report “Time until convergence, MSE [10^-3/voxel], and Resolution [Angstrom]). I think these statistics would be useful to report in your work, as they are more familiar with folks in the cryoEM field.
In Equation 3, how does one calculate Z, the normalization constant?
For the decoder, how large of the 3D space are you generating? What are the units? Are you using voxels to represent atomic density? What is the voxel size? Is it the same as on Page 11?
I think more description of the neural network architecture would be useful (more than what is reported on page 12).