This paper presents a diffusion method for generating terrains from a set of parameterized curves that characterize the landform features such as ridge lines, riverbeds or cliffs. Our approach provides the user with an intuitive vector-based feature-oriented control over the terrain. Different types of constraints (such as elevation, slope angle and roughness) can be attached to the curves so as to define the shape of the terrain. The terrain is generated from the curve representation by using an efficient multigrid diffusion algorithm. The algorithm can be efficiently implemented on the GPU, which allows the user to interactively create a vast variety of landscapes.