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 amongst others. Despite significant headway, the immense challenges in cryo-EM data analysis remain legion and intricately inter-disciplinary in nature, requiring insights from physicists, structural biologists, computer scientists, statisticians, and applied mathematicians. Meanwhile, recent next-generation volume reconstruction algorithms that combine generative modeling with end-to-end unsupervised deep learning techniques have shown promising results on simulated data, but still face considerable hurdles when applied to experimental cryo-EM images. In light of the proliferation of such methods and given the interdisciplinary nature of the task, we propose here a critical review of recent advances in the field of deep generative modeling for high resolution cryo-EM volume reconstruction. The present review aims to (i) compare and contrast these new methods, while (ii) presenting them from a perspective and using terminology familiar to scientists in each of the five aforementioned fields with no specific background in cryo-EM. The review begins with an introduction to the mathematical and computational challenges of deep generative models for cryo-EM volume reconstruction, along with an overview of the baseline methodology shared across this class of algorithms. Having established the common thread weaving through these different models, we provide a practical comparison of these state-of-the-art algorithms, highlighting their relative strengths and weaknesses, along with the assumptions that they rely on. This allows us to identify bottlenecks in current methods and avenues for future research.
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