Blind image inpainting aims to restore images degraded by unknown corruption, where the locations and shapes of missing regions are unspecified at inference time. Existing methods typically separate mask estimation and image restoration into sequential stages, which can lead to error propagation and poor integration of structural priors, especially when dealing with complex or diverse artifacts. In this paper, we present Dual-Prior Diffusion (DPDiff), a novel framework that addresses blind inpainting by jointly predicting corruption masks and reconstructing edge maps. This simultaneous prediction of dual priors complementarily rectifies one another, significantly reducing error accumulation and enabling robust, structure-aware restoration. Leveraging these learned priors, DPDiff guides a diffusion model to generate restored images that both preserve geometric fidelity and blend seamlessly with uncorrupted content. Extensive experiments demonstrate that DPDiff sets a new state-of-the-art on multiple blind inpainting benchmarks using only four diffusion timesteps, and generalizes strongly to related image restoration tasks such as image deraining and watermark removal.