  A common approach for out-of-distribution detection involves estimating an
underlying data distribution, which assigns a lower likelihood value to
out-of-distribution data. Normalizing flows are likelihood-based generative
models providing a tractable density estimation via dimension-preserving
invertible transformations. Conventional normalizing flows are prone to fail in
out-of-distribution detection, because of the well-known curse of
dimensionality problem of the likelihood-based models. According to the
manifold hypothesis, real-world data often lie on a low-dimensional manifold.
This study investigates the effect of manifold learning using normalizing flows
on out-of-distribution detection. We proceed by estimating the density on a
low-dimensional manifold, coupled with measuring the distance from the
manifold, as criteria for out-of-distribution detection. However, individually,
each of them is insufficient for this task. The extensive experimental results
show that manifold learning improves the out-of-distribution detection ability
of a class of likelihood-based models known as normalizing flows. This
improvement is achieved without modifying the model structure or using
auxiliary out-of-distribution data during training.
