We provide a novel approach for aligning geometric models using a dual graph structure where local features are mapping probabilities. Alignment of non-rigid structures is one of the most challenging computer vision tasks due to the high number of unknowns needed to model the correspondence. We have seen a leap forward using DNN models in template alignment and functional maps,but those methods fail for inter-class alignment where non-isometric deformations exist. Here we propose to rethink this task and use unrolling concepts on a dual graph structure - one for a forward map and one for a backward map,where the features are pulled back matching probabilities from the target into the source. We report state of the art results on stretchable domains' alignment in a rapid and stable solution for meshes and point clouds.