Generative Artificial Intelligence (AI) is a cutting-edge technology capable of producing text, images, and various media content leveraging generative models and user prompts. Between 2022 and 2023, generative AI surged in popularity with a plethora of applications spanning from AI-powered movies to chatbots. This paper investigates the potential of generative AI within the realm of the World Wide Web, specifically focusing on image generation. Web developers already harness generative AI to help craft text and images, while Web browsers might use it in the future to locally generate images for tasks such as repairing broken webpages, conserving bandwidth, and enhancing privacy. To explore this research area, this paper developed WebDiffusion, a tool that allows to simulate a Web powered by stable diffusion, a popular text-to-image model, from both a client and server perspective. Such a tool is the first of its kind, paving the way towards a futuristic world wide web where web images can be created using generative AI. WebDiffusion further supports crowdsourcing of user opinions, which is used to evaluate the quality and accuracy of 409 AI-generated images sourced from 60 webpages. Our findings suggest that generative AI is already capable of producing pertinent and high-quality Web images, even without requiring Web designers to manually input prompts, just by leveraging contextual information available within the webpages. However, direct in-browser image generation remains a challenge, as only highly powerful GPUs, such as the A40 and A100, can (partially) compete with classic image downloads. Nevertheless, this approach could be valuable for a subset of the images, for example, when fixing broken webpages or handling highly private content.