Conflicting views exist of how circuits of the antennal lobe, the insect equivalent of the olfactory bulb, translate input from olfactory receptor neurons (ORNs) into projection-neuron (PN) output. Synaptic connections between ORNs and PNs are one-to-one, yet PNs are more broadly tuned to odors than ORNs. The basis for this difference in receptive range remains unknown. Analyzing a Drosophila mutant lacking ORN input to one glomerulus, we show that some of the apparent complexity in the antennal lobe's output arises from lateral, interglomerular excitation of PNs. We describe a previously unidentified population of cholinergic local neurons (LNs) with multiglomerular processes. These excitatory LNs respond broadly to odors but exhibit little glomerular specificity in their synaptic output, suggesting that PNs are driven by a combination of glomerulus-specific ORN afferents and diffuse LN excitation. Lateral excitation may boost PN signals and enhance their transmission to third-order neurons in a mechanism akin to stochastic resonance.