Dealing with motion artifacts is a fundamental preprocessing step in magnetic resonance imaging (MRI). In this work, we present three novel methods to generate MRI phantoms for diffeomorphic motion which can be used to validate motion correction algorithms. Previous research efforts for diffeomorphic motion generation, employ a brute force approach in which random pixel/voxel displacements are repeatedly generated until a topologically valid displacement is found. Such methods are not only time consuming but also doesn’t guarantee a valid displacement. Our approach algorithmically ensures that the topological properties are always maintained resulting in guaranteed diffeomorphic motion with much faster runtime.