Information processing in the rodent hippocampus is fundamentally shaped by internally generated sequences (IGSs), expressed during two different network states: theta sequences, which repeat and reset at the ∼8 Hz theta rhythm associated with active behavior, and punctate sharp wave-ripple (SWR) sequences associated with wakeful rest or slow-wave sleep. A potpourri of diverse functional roles has been proposed for these IGSs, resulting in a fragmented conceptual landscape. Here, we advance a unitary view of IGSs, proposing that they reflect an inferential process that samples a policy from the animal's generative model, supported by hippocampus-specific priors. The same inference affords different cognitive functions when the animal is in distinct dynamical modes, associated with specific functional networks. Theta sequences arise when inference is coupled to the animal's action-perception cycle, supporting online spatial decisions, predictive processing, and episode encoding. SWR sequences arise when the animal is decoupled from the action-perception cycle and may support offline cognitive processing, such as memory consolidation, the prospective simulation of spatial trajectories, and imagination. We discuss the empirical bases of this proposal in relation to rodent studies and highlight how the proposed computational principles can shed light on the mechanisms of future-oriented cognition in humans.