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Diffeomorphic image registration, offering smooth transformation and topology preservation, is required in many medical image analysis tasks.Traditional methods impose certain modeling constraints on the space of admissible transformations and use optimization to find the optimal transformation between two images. Specifying the right space of admissible transformations is challenging: the registration quality can be poor if the space is too restrictive, while the optimization can be hard to solve if the space is too general. Recent learning-based methods, utilizing deep neural networks to learn the transformation directly, achieve fast inference, but face challenges in accuracy due to the difficulties in capturing the small local deformations and generalization ability. Here we propose a new optimization-based method named DNVF (Diffeomorphic Image Registration with Neural Velocity Field) which utilizes deep neural network to model the space of admissible transformations. A multilayer perceptron (MLP) with sinusoidal activation function is used to represent the continuous velocity field and assigns a velocity vector to every point in space, providing the flexibility of modeling complex deformations as well as the convenience of optimization. Moreover, we propose a cascaded image registration framework (Cas-DNVF) by combining the benefits of both optimization and learning based methods, where a fully convolutional neural network (FCN) is trained to predict the initial deformation, followed by DNVF for further refinement. Experiments on two large-scale 3D MR brain scan datasets demonstrate that our proposed methods significantly outperform the state-of-the-art registration methods.