Implementations are described herein for augmenting a traditional search session with stateful chat—via what will be referred to as a “generative companion”—to facilitate more interactive searching. In various implementations, a query may be received, e.g., from a client device operated by a user. Contextual information associated with the user or the client device may be retrieved. Generative model (GM) output may be generated based on processing, using a generative model, data indicative of the query and the contextual information.