In medical image analysis, anatomical landmarks usually contain strong prior knowledge of their structural information. In this paper, we propose to promote medical landmark localization by modeling the underlying landmark distribution via normalizing flows. Specifically, we introduce the flow-based landmark distribution prior as a learnable objective function into a regression-based landmark localization framework. Moreover, we employ an integral operation to make the mapping from heatmaps to coordinates differentiable to further enhance heatmap-based localization with the learned distribution prior. Our proposed Normalizing Flow-based Distribution Prior (NFDP) employs a straightforward backbone and non-problem-tailored architecture (i.e., ResNet18), which delivers high-fidelity outputs across three X-ray-based landmark localization datasets. Remarkably, the proposed NFDP can do the job with minimal additional computational burden as the normalizing flows module is detached from the framework on inferencing. As compared to existing techniques, our proposed NFDP provides a superior balance between prediction accuracy and inference speed, making it a highly efficient and effective approach. The source code of this paper is available at https://github.com/jacksonhzx95/NFDP.