We present a novel deep learning method, DDMReg, for accurate dMRI registration. In dMRI registration, the goal is to align brain anatomical structures while ensuring local fiber orientations consistency with the underlying white matter anatomy. DDMReg is an unsupervised method for deformable dMRI registration, without the need of non-rigidly pre-registered images and the corresponding deformation field as ground truth. We propose a novel registration architecture that leverages not only whole-brain information but also tract-specific fiber orientation information. We perform comparisons with four state-of-the-art methods on several independently acquired datasets. Experimental results show that DDMReg obtains highly improved registration performance.