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Generic image inpainting aims to complete a corrupted image by borrowing surrounding information, which barely generates novel content. By contrast, multi-modal inpainting provides more flexible and useful controls on the inpainted content, \eg, a text prompt can be used to describe an object with richer attributes, and a mask can be used to constrain the shape of the inpainted object rather than being only considered as a missing area. We propose a new diffusion-based model named SmartBrush for completing a missing region with an object using both text and shape-guidance. While previous work such as DALLE-2 and Stable Diffusion can do text-guided inapinting they do not support shape guidance and tend to modify background texture surrounding the generated object. Our model incorporates both text and shape guidance with precision control. To preserve the background better, we propose a novel training and sampling strategy by augmenting the diffusion U-net with object-mask prediction. Lastly, we introduce a multi-task training strategy by jointly training inpainting with text-to-image generation to leverage more training data. We conduct extensive experiments showing that our model outperforms all baselines in terms of visual quality, mask controllability, and background preservation.