Solid-solid displacive, structural phase transformations typically undergo a discrete structural change from a parent to a product phase. Coupling electron microscopy, three-dimensional atom probe, and first-principles computations, we present the first direct evidence of a novel mechanism for a coupled diffusional-displacive transformation in titanium-molybdenum alloys wherein the displacive component in the product phase changes continuously with changing composition. These results have implications for other transformations and cannot be explained by conventional theories.