Abstract: Panoramic image essentially acts as a pivotal role in emerging virtual reality and augmented reality scenarios; however, the generation of panoramic images are essentially challenging due to the intrinsic spherical geometry and spherical distortions caused by equirectangular projection (ERP). To address this, we start from the very basics of spherical manifold of panoramic images, and propose a novel spherical manifold convolution (SMConv) on $S^2$ manifold. Based on the SMConv operation, we propose a spherical manifold guided diffusion (SMGD) model for text-conditioned panoramic image generation, which can well accommodate the spherical geometry during generation. We further develop a novel evaluation method by calculating grouped Fréchet inception distance (FID) on cube-map projections, which can well reflect the quality of generated panoramic images, compared to existing methods that randomly crop ERP-distorted content. Experiment results demonstrate that our SMGD model achieves the state-of-the-art generation quality and accuracy, whilst retaining the shortest sampling time in the text-conditioned panoramic image generation task.