Being able to infer 3D structures from 2D images with geometric principles, vanishing points have been a well-recognized concept in 3D vision research. It has been widely used in autonomous driving, SLAM, and AR/VR for applications including road direction estimation, camera calibration, and camera pose estimation. Existing vanishing point detection methods often need to trade off between robustness, precision, and inference speed. In this paper, we introduce VaPiD, a novel neural network-based rapid Vanishing Point Detector that achieves unprecedented efficiency with learned vanishing point optimizers. The core of our method contains two components: a vanishing point proposal network that gives a set of vanishing point proposals as coarse estimations; and a neural vanishing point optimizer that iteratively optimizes the positions of the vanishing point proposals to achieve high-precision levels. Extensive experiments on both synthetic and real-world datasets show that our method provides competitive, if not better, performance as compared to the previous state-of-the-art vanishing point detection approaches, while being significantly faster.