The latest developments in Artificial Intelligence include diffusion generative models, quite popular tools which can produce original images both unconditionally and, in some cases, conditioned by some inputs provided by the user. Apart from implementation details, which are outside the scope of this work, all of the main models used to generate images are substantially based on a common theory which restores a new image from a completely degraded one. In this work we explain how this is possible by focusing on the mathematical theory behind them, i.e. without analyzing in detail the specific implementations and related methods. The aim of this work is to clarify to the interested reader what all this means mathematically and intuitively.

翻译：人工智能的最新进展包括扩散生成模型，这些流行工具能够无条件地或在某些情况下根据用户提供的输入条件生成原创图像。除了实现细节（这不在本文讨论范围内）之外，所有用于生成图像的主要模型都基本上基于一个共同的理论，该理论从完全退化的图像中恢复出新的图像。在本文中，我们通过关注其背后的数学理论来解释这是如何实现的，即不详细分析具体的实现及相关方法。本文旨在向感兴趣的读者从数学和直观的角度阐明这一切的含义。