Abstract Robustness is the reproducible development of a phenotype despite stochastic noise. It often involves tradeoffs with other performance metrics, but the mechanisms underlying such tradeoffs were largely unknown. An Arabidopsis flower robustly develops four sepals from four precisely positioned auxin maxima. The development related myb-like 1 ( drmy1) mutant generates noise in auxin signaling that disrupts robustness in sepal initiation. Here, we find that increased expression of CUP-SHAPED COTYLEDON1 ( CUC1 ), a boundary specification transcription factor, in drmy1 underlies this loss of robustness. CUC1 surrounds and amplifies stochastic auxin noise in drmy1 to form variably positioned auxin maxima and sepal primordia. Removing CUC1 from drmy1 provides time for noisy auxin signaling to resolve into four precisely positioned auxin maxima, restoring robust sepal initiation. However, removing CUC1 decreases the intensity of auxin maxima and slows down sepal initiation. Thus, CUC1 increases morphogenesis speed but impairs robustness against auxin noise. Further, using a computational model, we find that the observed phenotype can be explained by the effect of CUC1 in repolarizing PIN FORMED1 (PIN1), a polar auxin transporter. Lastly, our model predicts that reducing global growth rate improves developmental robustness, which we validate experimentally. Thus, our study illustrates a tradeoff between speed and robustness during development.