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 S2manifold inherent to panoramic images, and propose a novel spherical manifold convolution (SMConv) on S2manifold. 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. Codes are publicly available at https://github.com/chronos123/SMGD.

Panoramic image outpainting acts as a pivotal role in immersive content generation, allowing for seamless restoration and completion of panoramic content. Given the fact that the majority of generative outpainting solutions operates on planar images, existing methods for panoramic images address the sphere nature by soft regularisation during the end-to-end learning, which still fails to fully exploit the spherical content. In this paper, we set out the first attempt to impose the sphere nature in the design of diffusion model, such that the panoramic format is intrinsically ensured during the learning procedure, named as spherical-nested diffusion (SpND) model. This is achieved by employing spherical noise in the diffusion process to address the structural prior, together with a newly proposed spherical deformable convolution (SDC) module to intrinsically learn the panoramic knowledge. Upon this, the proposed method is effectively integrated into a pre-trained diffusion model, outperforming existing state-of-the-art methods for panoramic image outpainting. In particular, our SpND method reduces the FID values by more than 50\% against the state-of-the-art PanoDiffusion method. Codes are publicly available at \url{https://github.com/chronos123/SpND}.