Taking advantage of the well-characterized olfactory system of Drosophila, we derive a simple quantitative relationship between patterns of odorant receptor activation, the resulting internal representations of odors, and odor discrimination. Second-order excitatory and inhibitory projection neurons (ePNs and iPNs) convey olfactory information to the lateral horn, a brain region implicated in innate odor-driven behaviors. We show that the distance between ePN activity patterns is the main determinant of a fly's spontaneous discrimination behavior. Manipulations that silence subsets of ePNs have graded behavioral consequences, and effect sizes are predicted by changes in ePN distances. ePN distances predict only innate, not learned, behavior because the latter engages the mushroom body, which enables differentiated responses to even very similar odors. Inhibition from iPNs, which scales with olfactory stimulus strength, enhances innate discrimination of closely related odors, by imposing a high-pass filter on transmitter release from ePN terminals that increases the distance between odor representations.