In practical scenarios where training data is limited, many predictive signals in the data can be rather from some biases in data acquisition (i.e., less generalizable), so that one cannot prevent a model from co-adapting on such (so-called) “shortcut” signals: this makes the model fragile in various distribution shifts. To bypass such failure modes, we consider an adversarial threat model under a mutual information constraint to cover a wider class of perturbations in training. This motivates us to extend the standard information bottleneck to additionally model the nuisance information. We propose an autoencoder-based training to implement the objective, as well as practical encoder designs to facilitate the proposed hybrid discriminative-generative training concerning both convolutional- and Transformer-based architectures. Our experimental results show that the proposed scheme improves robustness of learned representations (remarkably without using any domain-specific knowledge), with respect to multiple challenging reliability measures. For example, our model could advance the state-of-the-art on a recent challenging OBJECTS benchmark in novelty detection by 78.4% -> 87.2% in AUROC, while simultaneously enjoying improved corruption, background and (certified) adversarial robustness. Code is available at https://github.com/jh-jeong/nuisance_ib.