Generative adversarial networks (GANs) have made great success in image inpainting yet still have difficulties tackling large missing regions. In contrast, iterative algorithms, such as autoregressive and denoising diffusion models, have to be deployed with massive computing resources for decent effect. To overcome the respective limitations, we present a novel spatial diffusion model (SDM) that uses a few iterations to gradually deliver informative pixels to the entire image, largely enhancing the inference efficiency. Also, thanks to the proposed decoupled probabilistic modeling and spatial diffusion scheme, our method achieves high-quality large-hole completion. On multiple benchmarks, we achieve new state-of-the-art performance. Code is released at this https URL