In this paper we propose a novel and robust approach for de-formable fusion using a metric defined in an appropriate sub-space which is adaptive to the image-content/image-modality. We adopt a graph-based formulation that assumes that intensities of corresponding pixels in the two image domains are related through an unknown piece-wise constant linear function. This relation is propagated to an appropriate sub-space (wavelets coefficients) where a criterion that couples the estimation of the deformation field with optimal transport function on the subspace and the smoothness of the deformation is considered. Message passing methods efficiently implemented using jump flooding are considered to get the optimal parameters of the deformation field and the transport function. Promising results are obtained in near real-time with a unique parameter setting.