Abstract: We consider the problem of quantization for surface graphs. In particular, we generalize the process of error diffusion to meshes and then compare different paths on the surface when used for error diffusion. We suggest paths for processing mesh elements that lead to better distributions of available neighbors for error diffusion. We demonstrate the potential benefit of error diffusion at several mesh processing applications: quantization of differential mesh coordinates, including an extension to animated geometry, and vertex subset selection for mesh simplification. These applications allow us to compare different paths objectively. We find that the linear time solution results in excellent overall performance, outperforming other traversals taken from the literature. We conclude that the proposed path can be taken as a starting point for any application of error diffusion on meshes.