We present Mask-GVAE, a variational generative model for blind denoising large discrete graphs, in which ”blind denoising” means we don’t require any supervision from clean graphs. We focus on recovering graph structures via deleting irrelevant edges and adding missing edges, which has many applications in real-world scenarios, for example, enhancing the quality of connections in a co-authorship network. Mask-GVAE makes use of the robustness in low eigenvectors of graph Laplacian against random noise and decomposes the input graph into several stable clusters. It then harnesses the huge computations by decoding probabilistic smoothed subgraphs in a variational manner. On a wide variety of benchmarks, Mask-GVAE outperforms competing approaches by a significant margin on PSNR and WL similarity.