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.
