3D scene perception demands a large amount of adverse-weather LiDAR data, yet the cost of LiDAR data collection presents a significant scaling-up challenge. To this end, a series of LiDAR simulators have been proposed. Yet, they can only simulate a single adverse weather with a single physical model, and the fidelity is quite limited. This paper presents WeatherGen, the first unified diverse-weather LiDAR data diffusion generation framework, significantly improving fidelity. Specifically, we first design a map-based data producer, which is capable of providing a vast amount of high-quality diverse-weather data for training purposes. Then, we utilize the diffusion-denoising paradigm to construct a diffusion model. Among them, we propose a spider mamba generator with the spider mamba scan to restore the disturbed diverse weather data gradually. The spider mamba models the feature interactions by scanning the LiDAR beam circle and central ray, excellently maintaining the physical structure of the LiDAR point cloud. Subsequently, we design a latent domain aligner following the generator to transfer real-world knowledge. Afterward, we devise a contrastive learning-based controller, which equips weather control signals with compact semantic knowledge through language supervision from CLIP, guiding the diffusion model in generating more discriminative data. Finally, we fine-tune WeatherGen with small-scale real-world data to further enhance its performance. Extensive evaluations on KITTI-360 and Seeing Through Fog demonstrate the high generation quality of WeatherGen. Through WeatherGen, we construct the mini-weather dataset, promoting the performance of the downstream task under adverse weather conditions.