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Dynamic medical imaging is usually limited in application due to the large radiation doses and longer image scanning and reconstruction times. Existing methods attempt to reduce the dynamic sequence by interpolating the volumes between the acquired image volumes. However, these methods are limited to either 2D images and/or are unable to support large variations in the motion between the image volume sequences. In this paper, we present a spatiotemporal volumetric interpolation network (SVIN) designed for 4D dynamic medical images. SVIN introduces dual networks: first is the spatiotemporal motion network that leverages the 3D convolutional neural network (CNN) for unsupervised parametric volumetric registration to derive spatiotemporal motion field from two-image volumes; the second is the sequential volumetric interpolation network, which uses the derived motion field to interpolate image volumes, together with a new regression-based module to characterize the periodic motion cycles in functional organ structures. We also introduce an adaptive multi-scale architecture to capture the volumetric large anatomy motions. Experimental results demonstrated that our SVIN outperformed state-of-the-art temporal medical interpolation methods and natural video interpolation methods that have been extended to support volumetric images. Our ablation study further exemplified that our motion network was able to better represent the large functional motion compared with the state-of-the-art unsupervised medical registration methods.