In this work we propose a novel method to correct echo planar imaging (EPI) distortions in diffusion MRI data acquired with reversed phase encoding directions ("blip-up blip-down" acquisitions). The transformation model is symmetric, diffeomorphic and capable of capturing large deformations. It can take advantage of a structural MRI target and include the contribution of diffusion weighted images, in addition to EPI images acquired without diffusion sensitization. The proposed correction significantly outperform existing strategies, assuring anatomically accurate characterization of the orientation, mean diffusivity, and anisotropy of white matter structures in the human brain.