Abstract Morphing structures are often engineered with stresses introduced into a flat sheet by leveraging structural anisotropy or compositional heterogeneity. Here, we identify a simple and universal diffusion-based mechanism to enable a transient morphing effect in structures with parametric surface grooves, which can be realized with a single material and fabricated using low-cost manufacturing methods (e.g., stamping, molding, and casting). We demonstrate from quantitative experiments and multiphysics simulations that parametric surface grooving can induce temporary asynchronous swelling or deswelling and can transform flat objects into designed, three-dimensional shapes. By tuning the grooving pattern, we can achieve both zero (e.g., helices) and nonzero (e.g., saddles) Gaussian curvature geometries. This mechanism allows us to demonstrate approaches that could improve the efficiency of certain food manufacturing processes and facilitate the sustainable packaging of food, for instance, by creating morphing pasta that can be flat-packed to reduce the air space in the packaging.