Quality control in additive manufacturing (AM) is vital for industrial applications in areas such as the automotive, medical and aerospace sectors. Geometric inaccuracies caused by shrinkage and deformations can compromise the life and performance of additively manufactured components. Such deviations can be quantified using Digital Volume Correlation (DVC), which compares the computer-aided design (CAD) model with the X-ray Computed Tomography (XCT) geometry of the components produced. However, accurate registration between the two modalities is challenging due to the absence of a ground truth or reference deformation field. In addition, the extremely large data size of high-resolution XCT volumes makes computation difficult. In this work, we present a deep learning-based approach for estimating voxel-wise deformations between CAD and XCT volumes. Our method uses a dynamic patch-based processing strategy to handle high-resolution volumes. In addition to the Dice Score, we introduce a Binary Difference Map (BDM) that quantifies voxel-wise mismatches between binarized CAD and XCT volumes to evaluate the accuracy of the registration. Our approach shows a 9.2\% improvement in the Dice Score and a 9.9\% improvement in the voxel match rate compared to classic DVC methods, while reducing the interaction time from days to minutes. This work sets the foundation for deep learning-based DVC methods to generate compensation meshes that can then be used in closed-loop correlations during the AM production process. Such a system would be of great interest to industries since the manufacturing process will become more reliable and efficient, saving time and material.