The challenge of defining a slot schema to represent the state of a task-oriented dialogue system is addressed by Slot Schema Induction (SSI), which aims to automatically induce slots from unlabeled dialogue data. Whereas previous approaches induce slots by clustering value spans extracted directly from the dialogue text, we demonstrate the power of discovering slots using a generative approach. By training a model to generate slot names and values that summarize key dialogue information with no prior task knowledge, our SSI method discovers high-quality candidate information for representing dialogue state. These discovered slot-value candidates can be easily clustered into unified slot schemas that align well with human-authored schemas. Experimental comparisons on the MultiWOZ and SGD datasets demonstrate that Generative Dialogue State Inference (GenDSI) outperforms the previous state-of-the-art on multiple aspects of the SSI task.