  Primordial black holes (PBHs) might be formed in the early Universe and could
comprise at least a fraction of the dark matter. Using the recently released
GWTC-2 dataset from the third observing run of the LIGO-Virgo Collaboration, we
investigate whether current observations are compatible with the hypothesis
that all black hole mergers detected so far are of primordial origin. We
constrain PBH formation models within a hierarchical Bayesian inference
framework based on deep learning techniques, finding best-fit values for
distinctive features of these models, including the PBH initial mass function,
the fraction of PBHs in dark matter, and the accretion efficiency. The presence
of several spinning binaries in the GWTC-2 dataset favors a scenario in which
PBHs accrete and spin up. Our results indicate that PBHs may comprise only a
fraction smaller than $0.3 \%$ of the total dark matter, and that the predicted
PBH abundance is still compatible with other constraints.
