  The IceCube Neutrino Observatory is a cubic-kilometer high-energy neutrino
detector deployed in the Antarctic ice. Two major event classes are
charged-current electron and muon neutrino interactions. In this contribution,
we discuss the inference of direction and energy for these classes using
conditional normalizing flows. They allow to derive a posterior distribution
for each individual event based on the raw data that can include systematic
uncertainties, which makes them very promising for next-generation
reconstructions. For each normalizing flow we use the differential entropy and
the KL-divergence to its maximum entropy approximation to interpret the
results. The normalizing flows correctly incorporate complex optical properties
of the Antarctic ice and their relation to the embedded detector. For showers,
the differential entropy increases in regions of high photon absorption and
decreases in clear ice. For muons, the differential entropy strongly correlates
with the contained track length. Coverage is maintained, even for low photon
counts and highly asymmetrical contour shapes. For high-photon counts, the
distributions get narrower and become more symmetrical, as expected from the
asymptotic theorem of Bernstein-von-Mises. For shower directional
reconstruction, we find the region between 1 TeV and 100 TeV to potentially
benefit the most from normalizing flows because of azimuth-zenith asymmetries
which have been neglected in previous analyses by assuming symmetrical
contours. Events in this energy range play a vital role in the recent discovery
of the galactic plane diffuse neutrino emission.
