Generative AI (Gen-AI) represents a major growth potential for the digital industry, a new stage in digital transformation through its many applications. Unfortunately, by accelerating the growth of digital technology, Gen-AI is contributing to the significant and multiple environmental damage caused by its sector. The question of the sustainability of IT must include this new technology and its applications, by measuring its environmental impact. To best respond to this challenge, we propose various ways of improving the measurement of Gen-AI's environmental impact. Whether using life-cycle analysis methods or direct measurement experiments, we illustrate our methods by studying Stable Diffusion a Gen-AI image generation available as a service. By calculating the full environmental costs of this Gen-AI service from end to end, we broaden our view of the impact of these technologies. We show that Gen-AI, as a service, generates an impact through the use of numerous user terminals and networks. We also show that decarbonizing the sources of electricity for these services will not be enough to solve the problem of their sustainability, due to their consumption of energy and rare metals. This consumption will inevitably raise the question of feasibility in a world of finite resources. We therefore propose our methodology as a means of measuring the impact of Gen-AI in advance. Such estimates will provide valuable data for discussing the sustainability or otherwise of Gen-AI solutions in a more transparent and comprehensive way. We intend to help this discussion by differentiating in our approach between the embodied and operational impacts of Gen-AI. In this way, we can consider the sustainability of models, as we already do for equipment.