Deep neural networks excel at image classification, but their performance is far less robust to input perturbations than human perception. In this work we explore whether this shortcoming may be partly addressed by incorporating brain-inspired recurrent dynamics in deep convolutional networks. We take inspiration from a popular framework in neuroscience: "predictive coding". At each layer of the hierarchical model, generative feedback "predicts" (i.e., reconstructs) the pattern of activity in the previous layer. The reconstruction errors are used to iteratively update the network’s representations across timesteps, and to optimize the network's feedback weights over the natural image dataset--a form of unsupervised training. We show that implementing this strategy into two popular networks, VGG16 and EfficientNetB0, improves their robustness against various corruptions and adversarial attacks. We hypothesize that other feedforward networks could similarly benefit from the proposed framework. To promote research in this direction, we provide an open-sourced PyTorch-based package called \textit{Predify}, which can be used to implement and investigate the impacts of the predictive coding dynamics in any convolutional neural network.