The Merriman-Bence-Osher Scheme, also known as Diffusion Generated Motion, is a simple algorithm for approximating mean curvature flow (MCF). The procedure alternates between diffusion and projection of a state function in such a way that its zero set approximates the solution of MCF. An advantage of this approach is that it naturally computes topological changes, like merging and breaking of solutions, without any additional steps. Originally proposed for hypersurfaces, the scheme is less well-understood when applied to submanifolds of higher codimension. Using a combination of rigorous analysis and numerical techniques, we characterize the convergence in the case of a space curve.