Generative diffusion models from a PDE perspective

Generating new images has become more common, anyone can easily generate
new images using a simple prompt. Although there are various techniques
such as autoencoders or GANs (Generative Adversarial Networks), the most
popular approach nowadays is to use diffusion models.
The goal of this presentation is to introduce the core idea of this
method, which consists of reversing a diffusion process. However,
reversing diffusion is an ill-posed problem. We will show how to bypass
this restriction by transforming a diffusion equation into a transport
equation. We then analyze how the generated density relates to the
original samples, proving that diffusion models (if done perfectly) do
not generalize.