The core network refers to a set of neural regions that have been consistently associated with episodic memory retrieval and episodic future simulation. This network is thought to support the constructive thought processes that allow the retrieval and flexible combination of stored information to reconstruct past and construct novel future experiences. Recent behavioral research points to an overlap between these constructive processes and those also engaged during divergent thinking—the ability to think creatively and generate novel ideas—but the extent to which they involve common neural correlates remains unclear. Using fMRI, we sought to address this question by assessing brain activity as participants recalled past experiences, simulated future experiences, or engaged in divergent thinking. Consistent with past work, we found that episodic retrieval and future simulation activated the core network compared with a semantic control condition. Critically, a triple conjunction of episodic retrieval, future simulation, and divergent thinking revealed common engagement of core network regions, including the bilateral hippocampus and parahippocampal gyrus, as well as other regions involved in memory retrieval (inferior frontal gyrus) and mental imagery (middle occipital gyrus). The results provide further insight into the roles of the hippocampus and the core network in episodic memory retrieval, future simulation, and divergent thinking and extend recent work highlighting the involvement of constructive episodic processes in creative cognition.