Developing tissues change shape, and tumors initiate spreading, through collective cell motility. Conserved mechanisms by which tissues initiate motility into their surroundings are not known. We investigated cytoskeletal regulators during collective invasion by mouse tumor organoids and epithelial MDCK acini undergoing branching morphogenesis. Inhibition of formins, but not Arp2/3, prevented the formation of migrating cell fronts in both cell types. MDCK cells depleted of the formin protein Dia1 formed polarized acini and could execute planar cell motility, either within the acinus or in 2D scattering assays. However, Dia1 was required to form protrusions into the collagen matrix. Live imaging of actin, myosin, and collagen in control acini revealed adhesions that deformed individual collagen fibrils, while Dia1-depleted acini exhibited unstable adhesions with minimal collagen deformation. This work identifies Dia1-mediated adhesions as essential regulators of tissue shape changes, through their role in focal adhesion maturation.