TOC

Reference:

Official links:

  1. PFGM (NeurIPS 2022)

    Paper: Poisson Flow Generative Models

    Github: https://github.com/Newbeeer/poisson_flow

Blog:

  1. An Introduction to Poisson Flow Generative Models

Main idea

The idea is inspired by the field of electrodynamics that Any distribution of electrons in a hyperplane generates an electric field (aka Poisson field) that transforms the distribution into a uniform angular distribution as the distribution evolves through time according to the dynamics defines by the field.

The key of PFGM.
Treating a data distribution as a charge distribution defines an electric field that transforms the distribution into a uniform hemisphere over time.

If we know the electric field (Poisson field) generated by a distribution, then we can start with points uniformly sampled on a hemisphere and run the dynamics in reverse time to recover the original data distribution. The law of physics, therefore, provide an invertible mapping between a simple distribution and the data distribution, yielding a means to generate novel data akin to normalizing flows.

The reverse process.
Uniformly sampled points on the hemisphere can be transformed into samples from the data distribution by evolving them backwards through the Poisson field generated by the data distribution.

Training process

We seek to model the dynamics of particles under the influence of the Poisson field generated by a data distribution.