Introduction

The

Probability-Flow ODE(PF-ODE)

Consistency model (CM)

Poisson Flow Generative Models(PFGM)

If we take a look at DDPM and DDIM, the trained neural network outputs a direction for a given input \((x_t, t)\) which means the status at a given time \(t\). For these diffusion based model, we expect the neural network can approximate the reverse diffusive steps. The recent paper () provided a different framework to formulate the process. Inspired by the gravitivity(or any physical quantity that follows inverse-square law), each example in the dataset can be view as a mass point(or particle) in the space and the entire dataset formed a gravity field. Intuitively, the generation process can be viewed as a random point, sampled far away from the dataset, moving within the gravity field and falls into some equilibrium point.

Formulation

In this setup, there is no explicit “forward process” and we can start from the backward process