Sensory systems are robust to many types of corrupting noise. However, the neural mechanisms that drive robustness are unclear. Empirical evidence suggests that top-down predictions are important for processing noisy stimuli, and the substantial feedback connections in primate sensory cortices have been proposed to facilitate these predictions. Here, we implement predictive dynamics in a large scale model of the human auditory system. Specifically, we augment a feedforward deep neural network trained on noisy speech classification with a recently introduced predictive feedback scheme. We find that predictive dynamics improve speech identification across several types of corrupting noise. These performance gains were associated with denoising of network representations and alterations in layer dimensionality. Finally, we find that the model captures brain data outside of the speech domain. Overall, this work demonstrates that predictive dynamics are a candidate mechanism for human auditory robustness and provides a testbed for hypotheses regarding the dynamics of auditory representations. Additionally, we discuss the potential for this framework to provide insight into robustness mechanisms across sensory modalities.