Deformable image registration can be time-consuming and often needs extensive parameterization to perform well on a specific application. We present a step towards a registration framework based on a three-dimensional convolutional neural network. The network directly learns transformations between pairs of three-dimensional images. The outputs of the network are three maps for the x, y, and z components of a thin plate spline transformation grid. The network is trained on synthetic random transformations, which are applied to a small set of representative images for the desired application. Training therefore does not require manually annotated ground truth deformation information. The methodology is demonstrated on public data sets of inspiration-expiration lung CT image pairs, which come with annotated corresponding landmarks for evaluation of the registration accuracy. Advantages of this methodology are its fast registration times and its minimal parameterization.