Stable Diffusion is a latent diffusion model, a kind of deep generative artificial neural network.
The development of Stable Diffusion was funded and shaped by the start-up company Stability AI. The technical license for the model was released by the CompVis group at Ludwig Maximilian University of Munich. Development was led by Patrick Esser of Runway and Robin Rombach of CompVis, who were among the researchers who had earlier invented the latent diffusion model architecture used by Stable Diffusion.
More detailed workflow explanation here.