  Thanks to the tractability of their likelihood, several deep generative
models show promise for seemingly straightforward but important applications
like anomaly detection, uncertainty estimation, and active learning. However,
the likelihood values empirically attributed to anomalies conflict with the
expectations these proposed applications suggest. In this paper, we take a
closer look at the behavior of distribution densities through the lens of
reparametrization and show that these quantities carry less meaningful
information than previously thought, beyond estimation issues or the curse of
dimensionality. We conclude that the use of these likelihoods for anomaly
detection relies on strong and implicit hypotheses, and highlight the necessity
of explicitly formulating these assumptions for reliable anomaly detection.
