Centerline graphs, crucial for path planning in autonomous driving, are traditionally learned using deterministic methods. However, these methods often lack spatial reasoning and struggle with occluded or invisible centerlines. Generative approaches, despite their potential, remain underexplored in this domain. We introduce LaneDiffusion, a novel generative paradigm for centerline graph learning. LaneDiffusion innovatively employs diffusion models to generate lane centerline priors at the Bird's Eye View (BEV) feature level, instead of directly predicting vectorized centerlines. Our method integrates a Lane Prior Injection Module (LPIM) and a Lane Prior Diffusion Module (LPDM) to effectively construct diffusion targets and manage the diffusion process. Furthermore, vectorized centerlines and topologies are then decoded from these prior-injected BEV features. Extensive evaluations on the nuScenes and Argoverse2 datasets demonstrate that LaneDiffusion significantly outperforms existing methods, achieving improvements of 4.2%, 4.6%, 4.7%, 6.4% and 1.8% on fine-grained point-level metrics (GEO F1, TOPO F1, JTOPO F1, APLS and SDA) and 2.3%, 6.4%, 6.8% and 2.1% on segment-level metrics (IoU, mAP{cf}, DET{l} and TOP_{ll}). These results establish state-of-the-art performance in centerline graph learning, offering new insights into generative models for this task.