The developmental basis for the generation of divergent leaf forms is largely unknown. Here we investigate this problem by studying processes that distinguish development of two related species: Arabidopsis thaliana, which has simple leaves, and Cardamine hirsuta, which has dissected leaves with individual leaflets. Using genetics, expression studies and cell lineage tracing, we show that lateral leaflet formation in C. hirsuta requires the establishment of growth foci that form after leaf initiation. These growth foci are recruited at the leaf margin in response to activity maxima of auxin, a hormone that polarizes growth in diverse developmental contexts. Class I KNOTTED1-like homeobox (KNOX) proteins also promote leaflet initiation in C. hirsuta, and here we provide evidence that this action of KNOX proteins is contingent on the ability to organize auxin maxima via the PINFORMED1 (PIN1) auxin efflux transporter. Thus, differential deployment of a fundamental mechanism polarizing cellular growth contributed to the diversification of leaf form during evolution.