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The majority of deep learning (DL) based deformable image registration methods use convolutional neural networks (CNNs) to estimate displacement fields from pairs of moving and fixed images. This, however, requires the convolutional kernels in the CNN to not only extract intensity features from the inputs but also understand image coordinate systems. We argue that the latter task is challenging for traditional CNNs, limiting their performance in registration tasks. To tackle this problem, we first introduce Coordinate Translator, a differentiable module that identifies matched features between the fixed and moving image and outputs their coordinate correspondences without the need for training. It unloads the burden of understanding image coordinate systems for CNNs, allowing them to focus on feature extraction. We then propose a novel deformable registration network, im2grid, that uses multiple Coordinate Translator's with the hierarchical features extracted from a CNN encoder and outputs a deformation field in a coarse-to-fine fashion. We compared im2grid with the state-of-the-art DL and non-DL methods for unsupervised 3D magnetic resonance image registration. Our experiments show that im2grid outperforms these methods both qualitatively and quantitatively.