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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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
02.08.2024
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| Subjects | |
| Online Access | Get full text |
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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). |
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| 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 |
| Author_xml | – sequence: 1 givenname: Manhyung surname: Han fullname: Han, Manhyung |
| BackLink | https://doi.org/10.48550/arXiv.2408.07285$$DView paper in arXiv |
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| Snippet | This note provides a critical review of the mathematical concepts underlying
the generalized diffusion denoising implicit model (gDDIM) and the exponential... |
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| Title | DDIM Redux: Mathematical Foundation and Some Extension |
| URI | https://arxiv.org/abs/2408.07285 |
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