We present a novel diffusion-based approach to generate synthetic histopathological Whole Slide Images (WSIs) at an unprecedented gigapixel scale. Synthetic WSIs have many potential applications: They can augment training datasets to enhance the performance of many computational pathology applications. They allow the creation of synthesized copies of datasets that can be shared without violating privacy regulations. Or they can facilitate learning representations of WSIs without requiring data annotations. Despite this variety of applications, no existing deep-learning-based method generates WSIs at their typically high resolutions. Mainly due to the high computational complexity. Therefore, we propose a novel coarse-to-fine sampling scheme to tackle image generation of high-resolution WSIs. In this scheme, we increase the resolution of an initial low-resolution image to a high-resolution WSI. Particularly, a diffusion model sequentially adds fine details to images and increases their resolution. In our experiments, we train our method with WSIs from the TCGA-BRCA dataset. Additionally to quantitative evaluations, we also performed a user study with pathologists. The study results suggest that our generated WSIs resemble the structure of real WSIs.