AI systems sometimes exhibit harmful unintended behaviors post-deployment. This is often despite extensive diagnostics and debugging by developers. Minimizing risks from models is challenging because the attack surface is so large. It is not tractable to exhaustively search for inputs that may cause a model to fail. Red-teaming and adversarial training (AT) are commonly used to make AI systems more robust. However, they have not been sufficient to avoid many real-world failure modes that differ from the ones adversarially trained on. In this work, we utilize latent adversarial training (LAT) to defend against vulnerabilities without generating inputs that elicit them. LAT leverages the compressed, abstract, and structured latent representations of concepts that the network actually uses for prediction. We use LAT to remove trojans and defend against held-out classes of adversarial attacks. We show in image classification, text classification, and text generation tasks that LAT usually improves both robustness and performance on clean data relative to AT. This suggests that LAT can be a promising tool for defending against failure modes that are not explicitly identified by developers.