Biological insights often depend on comparing conditions such as disease and health. Yet, we lack effective computational tools for integrating single-cell genomics data across conditions or characterizing transitions from normal to deviant cell states. Here, we present Decipher, a deep generative model that characterizes derailed cell-state trajectories. Decipher jointly models and visualizes gene expression and cell state from normal and perturbed single-cell RNA-seq data, revealing shared and disrupted dynamics. We demonstrate its superior performance across diverse contexts, including in pancreatitis with oncogene mutation, acute myeloid leukemia, and gastric cancer.