Denoising diffusion models have shown a powerful capacity for generating high-quality image samples by progressively removing noise. Inspired by this, we present a diffusion-based mesh denoiser that progressively removes noise from mesh. In general, the iterative algorithm of diffusion models attempts to manipulate the overall structure and fine details of target meshes simultaneously. For this reason, it is difficult to apply the diffusion process to a mesh denoising task that removes artifacts while maintaining a structure. To address this, we formulate a structure-preserving diffusion process. Instead of diffusing the mesh vertices to be distributed as zero-centered isotopic Gaussian distribution, we diffuse each vertex into a specific noise distribution, in which the entire structure can be preserved. In addition, we propose a topology-agnostic mesh diffusion model by projecting the vertex into multiple 2-D viewpoints to efficiently learn the diffusion using a deep network. This enables the proposed method to learn the diffusion of arbitrary meshes that have an irregular topology. Finally, the denoised mesh can be obtained via refinement based on 2-D projections obtained from reverse diffusion. Through extensive experiments, we demonstrate that our method outperforms the state-of-the-art mesh denoising methods in both quantitative and qualitative evaluations.