  The tremendous success of generative models in recent years raises the
question whether they can also be used to perform classification. Generative
models have been used as adversarially robust classifiers on simple datasets
such as MNIST, but this robustness has not been observed on more complex
datasets like CIFAR-10. Additionally, on natural image datasets, previous
results have suggested a trade-off between the likelihood of the data and
classification accuracy. In this work, we investigate score-based generative
models as classifiers for natural images. We show that these models not only
obtain competitive likelihood values but simultaneously achieve
state-of-the-art classification accuracy for generative classifiers on
CIFAR-10. Nevertheless, we find that these models are only slightly, if at all,
more robust than discriminative baseline models on out-of-distribution tasks
based on common image corruptions. Similarly and contrary to prior results, we
find that score-based are prone to worst-case distribution shifts in the form
of adversarial perturbations. Our work highlights that score-based generative
models are closing the gap in classification accuracy compared to standard
discriminative models. While they do not yet deliver on the promise of
adversarial and out-of-domain robustness, they provide a different approach to
classification that warrants further research.
