Endovascular interventions are minimally invasive procedures that utilize the vascular system to access anatomical regions deep within the body. Image-guided assistance provides valuable realtime information about the dynamic state of the vascular environment. However, the reliance on intra-operative 2D fluoroscopy images limits depth perception, prompting the demand for intra-operative 3D imaging. Existing image registration methods face difficulties in accurately incorporating tissue deformations compared to the pre-operative 3D model, particularly in a weakly-supervised manner. Additionally, reconstructing deformations from 2D to 3D space and presenting this intra-operative model visually to clinicians poses further complexities. To address these challenges, this study introduces a novel deformable model-to-image registration framework using deep learning. Furthermore, this research proposes a visualization method through augmented reality to provide guidance for endovascular interventions. This study utilized image data collected from nine patients who underwent Transcatheter Aortic Valve Implantation (TAVI) procedures. The registration results in 2D indicate that the proposed deformable model-to-image registration framework achieves a Modified Dice Similarity Coefficient (MDSC) value of 0.89 ± 0.02 and a Penalization of Deformations in Spare Space (PDSS) value of 0.04 ± 0.01, offering an improvement of 3.5% and 98.6% over the state-of-the-art image registration approach. Additionally, the accuracy of registration in 3D was evaluated using a dataset obtained from an intervention simulator, resulting in a Mean Absolute Error (MAE) of 1.51 ± 1.02 mm within the region of interest. Overall, the study validates the feasibility and accuracy of the proposed weakly-supervised deformable model-to-image registration framework, demonstrating its potential to provide intra-operative 3D imaging as intervention assistance in dynamic vascular environments.