Abstract: We propose a zero-shot method for generating images in arbitrary spaces (e.g., a sphere for $360^\circ$ panoramas and a mesh surface for texture) using a pretrained image diffusion model. The zero-shot generation of various visual content using a pretrained image diffusion model has been explored mainly in two directions. First, Diffusion Synchronization-performing reverse diffusion processes jointly across different projected spaces while synchronizing them in the target space-generates high-quality outputs when enough conditioning is provided, but it struggles in its absence. Second, Score Distillation Sampling-gradually updating the target space data through gradient descent-results in better coherence but often lacks detail. In this paper, we reveal for the first time the interconnection between these two methods while highlighting their differences. To this end, we propose $\texttt{StochSync}$, a novel approach that combines the strengths of both, enabling effective performance with weak conditioning. Our experiments demonstrate that $\texttt{StochSync}$ provides the best performance in $360^\circ$ panorama generation (where image conditioning is not given), outperforming previous finetuning-based methods, and also delivers comparable results in 3D mesh texturing (where depth conditioning is provided) with previous methods.