Interpreting chemical information and translating it into ethologically relevant output is a common challenge of olfactory systems across species. Are computations performed by olfactory circuits conserved across species to overcome these common challenges? To understand this, we compared odor responses in the locust antennal lobe (AL) and mouse olfactory bulb (OB). We found that odors activated nearly mutually exclusive neural ensembles during stimulus presentation (‘ON response’) and after stimulus termination (‘OFF response’). Strikingly, ON and OFF responses evoked by a single odor were anticorrelated with each other. ‘Inverted’ OFF responses enhanced contrast between odors experienced close together in time. Notably, OFF responses persisted long after odor termination in both AL and OB networks, indicating a form of short-term memory. Taken together, our results reveal key neurodynamic features underlying olfactory computations that are conserved across insect and mammalian olfactory systems.