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Modeling the dynamics of heart and lung tissue is challenging because the tissue deforms between data acquisitions. To reconstruct complete volumes, sample data captured at different times and locations must be combined. This paper presents a novel end-to-end, data driven framework for the complete reconstruction of deforming tissue volumes. This framework is a joint optimization over an undeformed tissue volume, a deformation map that describes tissue motion forgiven pose parameters (i.e. breathing and heartbeat), and an estimate of those parameters for each data acquisition. Tissue motion is modeled by deforming a reference volume with a cubic B-spline free form deformation, and we use Isomap to derive initial estimates of the pose of sample data. An iterative method is used to simultaneously solve for the reference volume and deformation map while updating the pose estimates. This same process is demonstrated on 4D CT lung data and heart/lung MR data.