Removing blur caused by moving objects is challenging, as the moving objects are usually significantly blurry while the static background remains clear. Existing methods that rely on local blur detection often suffer from inaccuracies and cannot generate satisfactory results when focusing solely on blurred regions. To overcome these problems, we first design a context-based local blur detection module that incorporates additional contextual information to improve the identification of blurry regions. Considering that modern smartphones are equipped with cameras capable of providing short-exposure images, we develop a blur-aware guided image restoration method that utilizes sharp structural details from short-exposure images, facilitating accurate reconstruction of heavily blurred regions. Furthermore, to restore images realistically and visually-pleasant, we develop a short-exposure guided diffusion model that explores useful features from short-exposure images and blurred regions to better constrain the diffusion process. Finally, we formulate the above components into a simple yet effective network, named ExpRDiff. Experimental results show that ExpRDiff performs favorably against state-of-the-art methods.