Developmental patterning relies on morphogen gradients, which generally involve feedback loops to buffer against perturbations caused by fluctuations in gene dosage and expression1. Although many gene components involved in such feedback loops have been identified, how they work together to generate a robust pattern remains unclear. Here we study the network of extracellular proteins that patterns the dorsal region of the Drosophila embryo by establishing a graded activation of the bone morphogenic protein (BMP) pathway. We find that the BMP activation gradient itself is robust to changes in gene dosage. Computational search for networks that support robustness shows that transport of the BMP class ligands (Scw and Dpp) into the dorsal midline by the BMP inhibitor Sog is the key event in this patterning process. The mechanism underlying robustness relies on the ability to store an excess of signalling molecules in a restricted spatial domain where Sog is largely absent. It requires extensive diffusion of the BMP-Sog complexes, coupled with restricted diffusion of the free ligands. We show experimentally that Dpp is widely diffusible in the presence of Sog but tightly localized in its absence, thus validating a central prediction of our theoretical study.