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. Moreover, during resting behavior, coactivation 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 build a cognitive map that stretches beyond direct experience. However, mnemonic links that reflect deviations from actual experience may also create distortions in a cognitive map. In the second half of the talk I will show that when learning is performed under elevated levels of noradrenaline, systematic distortions in a participant’s cognitive map can be measured using behaviour. These systematic distortions reflect maladaptive inferences which may be explained by unwanted coactivation or ‘runaway excitation’ between indirectly related memories.