DDIM Redux: Mathematical Foundation and Some Extension

Fuente: arXiv
Guardado en:
Detalles Bibliográficos
Autor principal: Han, Manhyung
Formato: Preprint
Publicado: 2024
Materias:
Acceso en línea:
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
_version_ 1866910565114314752
author Han, Manhyung
author_facet Han, Manhyung
contents This note provides a critical review of the mathematical concepts underlying the generalized diffusion denoising implicit model (gDDIM) and the exponential integrator (EI) scheme. We present enhanced mathematical results, including an exact expression for the reverse trajectory in the probability flow ODE and an exact expression for the covariance matrix in the gDDIM scheme. Furthermore, we offer an improved understanding of the EI scheme's efficiency in terms of the change of variables. The noising process in DDIM is analyzed from the perspective of non-equilibrium statistical physics. Additionally, we propose a new scheme for DDIM, called the principal-axis DDIM (paDDIM).
format Preprint
id arxiv_https___arxiv_org_abs_2408_07285
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle DDIM Redux: Mathematical Foundation and Some Extension
Han, Manhyung
Machine Learning
This note provides a critical review of the mathematical concepts underlying the generalized diffusion denoising implicit model (gDDIM) and the exponential integrator (EI) scheme. We present enhanced mathematical results, including an exact expression for the reverse trajectory in the probability flow ODE and an exact expression for the covariance matrix in the gDDIM scheme. Furthermore, we offer an improved understanding of the EI scheme's efficiency in terms of the change of variables. The noising process in DDIM is analyzed from the perspective of non-equilibrium statistical physics. Additionally, we propose a new scheme for DDIM, called the principal-axis DDIM (paDDIM).
title DDIM Redux: Mathematical Foundation and Some Extension
topic Machine Learning
url https://arxiv.org/abs/2408.07285