arXiv:2610.20282v1 Announce Type: new Abstract: A generative site-specific beam prediction (Beam-STeP) method is proposed. Spatial priors from site-specific propagation and mobility information are jointly exploited with temporal priors from historical beam observations for beam prediction. To address the beam prediction ambiguity from multimodal spatio-temporal priors, the generative model is adopted, where a history-conditioned diffusion model is proposed to learn the multimodal conditional distribution of future beamforming vectors. Multiple beam candidates are sampled from the distribution using a denoising diffusion implicit model (DDIM). The candidate with the highest received power is then selected for transmission. Simulation results across three urban scenarios demonstrate that: i) Beam-STeP generally achieves higher normalized beamforming gains than the baselines under the same probing budget, particularly as beam prediction progresses; ii) site-specific propagation and mobility priors improve recursive beam prediction performance; and iii) DDIM sampling enables a flexible gain-latency trade-off.