DDIM Redux: Mathematical Foundation and Some Extension

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 fl...

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Published inarXiv.org
Main Author Han, Manhyung
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 03.08.2024
Subjects
Covariance matrix
Statistical analysis
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Abstract 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).
AbstractList 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).
Author Han, Manhyung
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Statistical analysis
Title DDIM Redux: Mathematical Foundation and Some Extension
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