dc.contributor.advisor |
Joo, Kyungdon |
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dc.contributor.author |
Yoon, Eunbi |
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dc.date.accessioned |
2024-04-11T15:20:05Z |
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dc.date.available |
2024-04-11T15:20:05Z |
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dc.date.issued |
2024-02 |
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dc.description.abstract |
Lévy-Itô Models belong to the category of score-based generative models, utilizing isotropic a-stable Lévy processes. Isotropic a-stable Lévy processes follows heavy-tailed distribution and possess dis- continuous paths, setting them apart from the light-tailed and continuous-path attributes of Brownian motion, which is commonly employed for injecting noise in traditional diffusion models. This paper focuses on the theoretical foundations required to derive the Lévy-Itô Models. It derives exact time- reversal formula of Stochastic differential equations (SDEs) driven by Lévy processes. It expands the concept of denoising score matching to incorporate the fractional score function version, which plays a crucial role in the drift term of the time-reversal formula for SDEs driven by an isotropic a-stable Lévy process. By computing the fractional score function of the transition density function, it can stabilizes the training of the fractional score models. Furthermore, this paper introduces a sampling method by leveraging the semi-linear structure in time-reversal SDEs. The theoretical analysis demonstrates that this sampling method converges for the Wasserstein-2 distance to a data distribution. In experiments, we show that Lévy-Itô models perform comparably to existing diffusion models on various image datasets while exhibiting a faster convergence rate and mitigating mode-collapse issues. |
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dc.description.degree |
Master |
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dc.description |
Graduate School of Artificial Intelligence |
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dc.identifier.uri |
https://scholarworks.unist.ac.kr/handle/201301/82159 |
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dc.identifier.uri |
http://unist.dcollection.net/common/orgView/200000743424 |
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dc.language |
ENG |
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dc.publisher |
Ulsan National Institute of Science and Technology |
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dc.rights.embargoReleaseDate |
9999-12-31 |
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dc.rights.embargoReleaseTerms |
9999-12-31 |
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dc.title |
Exploring theoretical perspective of Lévy itô model |
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dc.type |
Thesis |
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