Noise scheduling and linear dynamics in diffusion models on Lie groups
This work provides theoretical insights into diffusion processes on Lie groups, relevant for lattice gauge theory applications, but is incremental in nature.
The paper investigates noise scheduling in diffusion models on Lie groups, showing that a specific schedule leads to linear decay of the Wilson action expectation, a behavior that arises naturally in this setting compared to Euclidean models requiring explicit drift.
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.