The cellular homeostasis requires precise control of membrane shape and lipid phases. The membrane curvature likely sorts lipids and proteins to regulate the membrane composition of <100-nm radius endocytic pits and viral buds. However, the interplay between membrane curvature and local membrane composition is poorly understood at the nanoscale. Here, we employed single-molecule localization microscopy to observe single-lipid diffusion in model bilayers with varying lipid compositions, phase, temperature, and nanoscale membrane curvature. Engineered membrane buds were observed for the creation of lateral compositional heterogeneity in otherwise homogeneous membranes. Membrane curvature recruited liquid-disordered lipid phases in phase-separated membranes and altered the diffusion of the lipids. Supported lipid bilayers were created over 50-nm radius nanoparticles to engineer nanoscale membrane curvature that mimics the size of naturally occurring endocytic pits and viral buds. The disorder-preferring lipids sorted to the nanoscale curvature at all temperatures, but only when embedded in a membrane capable of sustaining liquid-liquid phase separation at low temperatures. This result suggests that lipid sorting by the membrane curvature was only possible when coupled with lipid phase separation. The curvature affected the local membrane composition most strongly when the curvature was locally surrounded by a liquid-ordered phase typically associated with a stiffer bending modulus. The curvature-induced sorting of lipid phases was quantified by the sorting of disorder-preferring fluorescent lipids, single-lipid diffusion measurements, and simulations that couple the lipid phase separation to the membrane shape. Unlike single-component membranes, lipids in phase-separated membranes demonstrated faster diffusion on curved membranes than the surrounding, flat membrane. These results demonstrate that curvature-induced membrane compositional heterogeneity can be achieved by collective behavior with lipid phase separation when single-molecule properties (i.e., packing parameter) are insufficient. These results support the hypothesis that the coupling of lipid phases and membrane shape may yield lateral membrane composition heterogeneities with functional consequences.SUMMARYNanoscale membrane curvature couples to lipid phase separationMembrane curvature concentrates the liquid-disorder preferring lipidsIn ternary mixtures, single-lipids diffuse faster in curved vs. flat membranesPhase separation induced by curvature propagated onto the surrounding planar bilayer