Every day we make decisions critical for adaptation and survival. We repeat actions with known consequences. But we can also infer associations between loosely related events to infer and imagine the outcome of entirely novel choices. In the first part of the talk I will show that during successful inference, the mammalian brain uses a hippocampal prospective code to forecast temporally structured learned associations. During periods of rest, co-activation of hippocampal cells in sharp-wave/ripples represent inferred relationships that include reward, thereby “joining-the-dots” between events that have not been observed together but lead to profitable outcomes. Computing mnemonic links in this manner may provide an important mechanism to infer new relationships. In the second part of the talk I will show how this hippocampal computation influences neocortex, by providing a generative training signal to build a deep internal model of the world that extends across the cortical hierarchy.