Controllable spherical panoramic image generation holds substantial applicative potential across a variety of domains. However, it remains a challenging task due to the inherent spherical distortion and geometry characteristics, resulting in low-quality content generation. In this paper, we introduce a novel framework of SphereDiffusion to address these unique challenges, for better generating high-quality and precisely controllable spherical panoramic images. For the spherical distortion characteristic, we embed the semantics of the distorted object with text encoding, then explicitly construct the relationship with text-object correspondence to better use the pre-trained knowledge of the planar images. Meanwhile, we employ a deformable technique to mitigate the semantic deviation in latent space caused by spherical distortion. For the spherical geometry characteristic, in virtue of spherical rotation invariance, we improve the data diversity and optimization objectives in the training process, enabling the model to better learn the spherical geometry characteristic. Furthermore, we enhance the denoising process of the diffusion model, enabling it to effectively use the learned geometric characteristic to ensure the boundary continuity of the generated images. With these specific techniques, experiments on Structured3D dataset show that SphereDiffusion significantly improves the quality of controllable spherical image generation and relatively reduces around 35% FID on average.