Models that are nearly indistinguishable on in-distribution data can behave very differently under distribution shift. We introduce Perturb-and-Correct (P&C), a post-hoc method for constructing epistemically diverse predictors from a single pretrained network. P&C applies random hidden-layer perturbations with a least-squares correction in the following affine layer, producing predictors that agree on calibration data while remaining free to disagree away from it. We analyze this mechanism through the post-correction residual that remains in the activation of the layer corrected using calibration data, yielding a leverage-based preservation bound and a covariance interpretation of ensemble disagreement. Empirically, P&C achieves a strong ID/OOD tradeoff across MuJoCo dynamics prediction and CIFAR-10 OOD detection, and scales to a pretrained ViT-B/16 on ImageNet-1K. In matched comparisons with Deep Ensembles, P&C substantially reduces construction and storage cost. Our findings highlight the potential in further exploiting overparameterization as a strength of deep learning models.

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