In this work, we consider the task of pairwise cross-modality image registration, which may benefit from exploiting additional images available only at training time from an additional modality that is different to those being registered. As an example, we focus on aligning intra-subject multiparametric Magnetic Resonance (mpMR) images, between T2-weighted (T2w) scans and diffusion-weighted scans with high b-value (DWI [Formula: see text]). For the application of localising tumours in mpMR images, diffusion scans with zero b-value (DWI [Formula: see text]) are considered easier to register to T2w due to the availability of corresponding features. We propose a learning from privileged modality algorithm, using a training-only imaging modality DWI [Formula: see text], to support the challenging multi-modality registration problems. We present experimental results based on 369 sets of 3D multiparametric MRI images from 356 prostate cancer patients and report, with statistical significance, a lowered median target registration error of 4.34 mm, when registering the holdout DWI [Formula: see text] and T2w image pairs, compared with that of 7.96 mm before registration. Results also show that the proposed learning-based registration networks enabled efficient registration with comparable or better accuracy, compared with a classical iterative algorithm and other tested learning-based methods with/without the additional modality. These compared algorithms also failed to produce any significantly improved alignment between DWI [Formula: see text] and T2w in this challenging application.