LiDAR and 2D camera calibration is attracting a growing interest in the domain of machine or deep learning with a wide range of application areas, including autonomous driving. Combining these two sensor suits creates a reliable referenced environment for 3D object detection. However, the combination into a unified representation presents challenges due to the disparities in the extrinsic characteristics of the sensors. Thus, the reliability and robustness of such systems are significantly reliant on calibration. This paper proposes a Camera/LiDAR calibration network via attention cost volume using monocular images and depth information. The architecture improves upon previously proposed architectures that take monocular images and output a 6 DoF (degree of freedom) rigid body transformation. The estimation of the latter is both the estimation of the extrinsic parameters and the action of extrinsic calibration. In previous works, the training was against photometric consistency and point cloud distance. In the new proposed architecture, the photometric loss is dropped; only point cloud distance is considered. The paper follows a strict geometric supervised learning without the direct estimation of the actual calibration parameters of the training dataset. In other words, the training process is agnostic to the extrinsic parameters and the extrinsic camera-LiDAR calibration is approached as an iterative closest point (ICP) problem. To ensure regularization and avoid overfitting, we perform dynamic miscalibration injection at training time and elastic net regularization (L1 and L2 penalization) in addition to multiple-stage dropouts. We demonstrate the superiority of our networks on a diverse set of hardware setups with different camera intrinsic and camera/LiDAR extrinsic parameters. KITTI 2011/09/26 is used for training and validation, while tests are performed on KITTI 2011/09/30, the odometry challenge, and the Waymo datasets.