Autonomous underwater vehicles (AUVs) are essential for various applications, including oceanographic surveys, underwater mapping, and infrastructure inspections. Accurate and robust navigation are critical to completing these tasks. To this end, a Doppler velocity log (DVL) and inertial sensors are fused together. Recently, a model-based approach demonstrated the ability to extract the vehicle acceleration vector from DVL velocity measurements. Motivated by this advancement, in this paper we present an end-to-end deep learning approach to estimate the AUV acceleration vector based on past DVL velocity measurements. Based on recorded data from sea experiments, we demonstrate that the proposed method improves acceleration vector estimation by more than 65% compared to the model-based approach by using data-driven techniques. As a result of our data-driven approach, we can enhance navigation accuracy and reliability in AUV applications, contributing to more efficient and effective underwater missions through improved accuracy and reliability.