Accurate localization serves as an important component in autonomous driving systems. Traditional rule-based localization involves many standalone modules, which is theoretically fragile and requires costly hyperparameter tuning, therefore sacrificing the accuracy and generalization. In this paper, we propose an end-to-end visual localization system, RAVE, in which the surrounding images are associated with the HD map data to estimate pose. To ensure high-quality observations for localization, a low-rank flow-based prior fusion module (FLORA) is developed to incorporate misaligned map prior into the perceived BEV features. Pursuing a balance among efficiency, interpretability, and accuracy, a hierarchical localization module is proposed, which efficiently estimates poses through a decoupled BEV neural matching-based pose solver (DEMA) using rasterized HD map, and then refines the estimation through a Transformer-based pose regressor (POET) using vectorized HD map. The experimental results demonstrate that our method can perform robust and accurate localization under varying environmental conditions while running efficiently.