Deep generative models (DGMs) seem a natural fit for detecting\nout-of-distribution (OOD) inputs, but such models have been shown to assign\nhigher probabilities or densities to OOD images than images from the training\ndistribution. In this work, we explain why this behavior should be attributed\nto model misestimation. We first prove that no method can guarantee performance\nbeyond random chance without assumptions on which out-distributions are\nrelevant. We then interrogate the typical set hypothesis, the claim that\nrelevant out-distributions can lie in high likelihood regions of the data\ndistribution, and that OOD detection should be defined based on the data\ndistribution's typical set. We highlight the consequences implied by assuming\nsupport overlap between in- and out-distributions, as well as the arbitrariness\nof the typical set for OOD detection. Our results suggest that estimation error\nis a more plausible explanation than the misalignment between likelihood-based\nOOD detection and out-distributions of interest, and we illustrate how even\nminimal estimation error can lead to OOD detection failures, yielding\nimplications for future work in deep generative modeling and OOD detection.\n