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A common approach for out-of-distribution detection involves estimating anunderlying data distribution, which assigns a lower likelihood value toout-of-distribution data. Normalizing flows are likelihood-based generativemodels providing a tractable density estimation via dimension-preservinginvertible transformations. Conventional normalizing flows are prone to fail inout-of-distribution detection, because of the well-known curse ofdimensionality problem of the likelihood-based models. According to themanifold hypothesis, real-world data often lie on a low-dimensional manifold.This study investigates the effect of manifold learning using normalizing flowson out-of-distribution detection. We proceed by estimating the density on alow-dimensional manifold, coupled with measuring the distance from themanifold, as criteria for out-of-distribution detection. However, individually,each of them is insufficient for this task. The extensive experimental resultsshow that manifold learning improves the out-of-distribution detection abilityof a class of likelihood-based models known as normalizing flows. Thisimprovement is achieved without modifying the model structure or usingauxiliary out-of-distribution data during training.

Out-of-distribution detection using normalizing flows on the data manifold