Auditing trained deep learning (DL) models prior to deployment is vital in preventing unintended consequences. One of the biggest challenges in auditing is in understanding how we can obtain human-interpretable specifications that are directly useful to the end-user. We address this challenge through a sequence of semantically-aligned unit tests, where each unit test verifies whether a predefined specification (e.g., accuracy over 95%) is satisfied with respect to controlled and semantically aligned variations in the input space (e.g., in face recognition, the angle relative to the camera). We perform these unit tests by directly verifying the semantically aligned variations in an interpretable latent space of a generative model. Our framework, AuditAI, bridges the gap between interpretable formal verification and scalability. With evaluations on four different datasets, covering images of towers, chest X-rays, human faces, and ImageNet classes, we show how AuditAI allows us to obtain controlled variations for verification and certified training while addressing the limitations of verifying using only pixel-space perturbations.