We propose a 3D shape generation framework (SDF-Diffusion in short) that uses denoising diffusion models with continuous 3D representation via signed distance fields (SDF). Unlike most existing methods that depend on discontinuous forms, such as point clouds, SDF-Diffusion generates high-resolution 3D shapes while alleviating memory issues by separating the generative process into two-stage: generation and super-resolution. In the first stage, a diffusion-based generative model generates a low-resolution SDF of 3D shapes. Using the estimated low-resolution SDF as a condition, the second stage diffusion model performs super-resolution to generate high-resolution SDF. Our framework can generate a high-fidelity 3D shape despite the extreme spatial complexity. On the ShapeNet dataset, our model shows competitive performance to the state-of-the-art methods and shows applicability on the shape completion task without modification.