Noise scheduling and linear dynamics in diffusion models on Lie groups

TL;DR

This paper explores how noise scheduling affects diffusion processes on Lie groups, revealing that certain schedules induce linear decay in Wilson action, with implications for lattice gauge theory.

Contribution

It demonstrates that a specific noise schedule naturally produces linear decay in Wilson action in Lie group diffusion models, unlike Euclidean models.

Findings

A particular noise schedule causes linear decay of Wilson action over diffusion time.

Linear decay occurs naturally in Lie groups without explicit drift design.

Comparison shows Euclidean models need explicit drift for similar behavior.

Abstract

We investigate the role of the noise schedule in diffusion processes on Lie groups, with particular emphasis on applications to lattice gauge theory. We show that a specific noise schedule leads to a linear decay of the expectation value of the Wilson action as a function of diffusion time. We compare this with Euclidean diffusion models, where such behavior requires an explicitly designed drift term, while in the Lie-group setting it arises naturally.