Development of spatial patterns in multicellular organisms depends on gradients in the concentration of signaling molecules that control gene expression. In the Drosophila embryo, Bicoid (Bcd) morphogen controls cell fate along 70% of the anteroposterior axis but is translated from mRNA localized at the anterior pole. Gradients of Bcd and other morphogens are thought to arise through diffusion, but this basic assumption has never been rigorously tested in living embryos. Furthermore, because diffusion sets a relationship between length and time scales, it is hard to see how patterns of gene expression established by diffusion would scale proportionately as egg size changes during evolution. Here, we show that the motion of inert molecules through the embryo is well described by the diffusion equation on the relevant length and time scales, and that effective diffusion constants are essentially the same in closely related dipteran species with embryos of very different size. Nonetheless, patterns of gene expression in these different species scale with egg length. We show that this scaling can be traced back to scaling of the Bcd gradient itself. Our results, together with constraints imposed by the time scales of development, suggest that the mechanism for scaling is a species-specific adaptation of the Bcd lifetime.