Generative Diffusion From An Action Principle

TL;DR

This paper introduces a physics-inspired perspective on generative diffusion models, framing score matching as an action principle, which unifies various diffusion approaches and enhances understanding of their theoretical foundations.

Contribution

It presents a novel derivation of score matching from an action principle, linking diffusion models to concepts in physics and unifying different classes of these models.

Findings

Score matching can be derived from an action principle.

The approach connects diffusion models to optimal control theory.

Unification of different diffusion model classes is demonstrated.

Abstract

Generative diffusion models synthesize new samples by reversing a diffusive process that converts a given data set to generic noise. This is accomplished by training a neural network to match the gradient of the log of the probability distribution of a given data set, also called the score. By casting reverse diffusion as an optimal control problem, we show that score matching can be derived from an action principle, like the ones commonly used in physics. We use this insight to demonstrate the connection between different classes of diffusion models.