Image fusion-guided interventions often require planning MR/CT and interventional U/S images to be registered in realtime. Organ motion, patient breathing and inconsistent ultrasound probe positioning during intervention, all contribute to the challenges of real-time 3D deformable registration, where alignment accuracy and computation time are often mutual trade-offs. In this work, we propose a novel framework to align planning and interventional 3D U/S by training patientspecific deep-deformation models (PsDDM) at the planning stage. During intervention, planning 3D U/S volumes are efficiently warped onto the interventional 3D U/S volumes using the trained deep-deformation model, thus enabling the transfer of other modality (planning MR/CT) information in real-time on interventional images. The alignment of planning MR/CT to planning U/S is not time-critical as these can be aligned before the intervention with desired accuracy using any known multimodal deformable registration method. The feasibility of training PsDDM is shown on liver U/S data acquired with a custom-built MR-compatible, hands-free 3D ultrasound probe that allows simultaneous acquisition of planning MR and U/S. Liver U/S volumes exhibit large motion in time due to respiration and therefore serve as a good anatomy to quantify the accuracy of the PsDDM. For quantitative evaluation of the PsDDM, a large vessel bifurcation was manually annotated on 9 U/S volumes that were not used for training the PsDDM but from the same subject. Mean target registration error (TRE) between the centroids was 0.84mm ± 0.39mm, mean Hausdorff distance (HD) was 1.80mm ± 0.29mm and mean surface distance (MSD) was 0.44mm ± 0.06mm for all volumes. In another experiment, the PsDDM was trained using liver volumes from one scanning session, while the model was tested on data from a separate scanning session of the same patient, for which qualitative alignment results were presented.