Digital Elevation Model (DEM) plays a fundamental role in remote sensing and photogrammetry. Enhancing the quality of DEM is crucial for various applications. Although multiple types of defects may appear simultaneously in the same DEM, they are commonly addressed separately. Most existing approaches only aim to fill the DEM voids, or apply super-resolution to the intact DEM. This paper introduces a unified generative model that simultaneously addresses voids and low-resolution problems, rather than taking two separate measures. The proposed approach presents the DEM Stochastic Differential Equation (DEM-SDE) for unified DEM quality enhancement. The DEM degradation of downsampling and random voids adding is modeled as the SDE forwarding, and the restoration is achieved by simulating the corresponding revert process. Conditioned on the terrain feature, and adopting efficient submodules with lightweight channel attention, DEM-SDE simultaneously enhances the DEM quality with an efficient process for training. The experiments show that DEM-SDE method achieves highly competitive performance in simultaneous super-resolution and void filling compared to the state-of-the-art work. DEM-SDE also manifests robustness for larger DEM patches.