Diverse image completion, a problem of generating various ways of filling incomplete regions (i.e. holes) of an image, has made remarkable success. However, managing input images with large holes is still a challenging problem due to the corruption of semantically important structures. In this paper, we tackle this problem by incorporating explicit structural guidance. We propose a structure-guided diffusion model (SGDM) for the large-hole diverse completion problem. Our proposed SGDM consists of a structure generator and a texture generator, which are both diffusion probabilistic models (DMs). The structure generator generates an edge image representing a plausible structure within the holes, which is later used to guide the texture generation process. To jointly train these two generators, we design a strategy that combines optimal Bayesian denoising and a momentum framework. In addition to the quality improvement, auxiliary edge images generated by the structure generator can be manually edited to allow user-guided image editing. Our experiments using datasets of faces (CelebA-HQ) and natural scenes (Places) show that our method achieves a comparable or superior trade-off between visual quality and diversity compared to other state-of-the-art methods.