To generate data, you need to know the probability distribution of a dataset. This is in general unknown. The method called "normalizing flows" starts with a simple distribution that we do know exactly, and learns how to turn the simple distribution into the data distribution through a series of transformations. If we know these transformations, then we can generate data from the data distribution by sampling from the simple distribution and passing it through the transformations.

Normalizing flows are a general approach to generative AI - how to actually learn the transformations and what they look like depends on the particular method. With PFGMs, the authors find that the laws of physics define these transformations. If we start with a simple distribution, we can transform it into the data distribution by imagining the data points are electrons and moving them according to the electric field they generate.