  Recent breakthroughs in high-resolution imaging of biomolecules in solution
with cryo-electron microscopy (cryo-EM) have unlocked new doors for the
reconstruction of molecular volumes, thereby promising further advances in
biology, chemistry, and pharmacological research. Recent next-generation volume
reconstruction algorithms that combine generative modeling with end-to-end
unsupervised deep learning techniques have shown promising preliminary results,
but still face considerable technical and theoretical hurdles when applied to
experimental cryo-EM images. In light of the proliferation of such methods, we
propose here a critical review of recent advances in the field of deep
generative modeling for cryo-EM volume reconstruction. The present review aims
to (i) unify and compare these new methods using a consistent statistical
framework, (ii) present them using a terminology familiar to machine learning
researchers and computational biologists with no specific background in
cryo-EM, and (iii) provide the necessary perspective on current advances to
highlight their relative strengths and weaknesses, along with outstanding
bottlenecks and avenues for improvements in the field. This review might also
raise the interest of computer vision practitioners, as it highlights
significant limits of deep generative models in low signal-to-noise regimes --
therefore emphasizing a need for new theoretical and methodological
developments.
