In this seminar, I will provide an overview of diffusion generative models, inverse problems, and their applications in solving such problems. Furthermore, I will present a novel interpretation of diffusion generative models and their translation to inverse problems. In collaboration with Hyungjin Chung and Dohoon Ryu, we propose that when data lies in a low-dimensional structure, the set of data with intermediate noise represents the interpolating manifold between the data manifold and the hypersphere of pure noise. Our new method, which respects this geometry, outperforms previous methods, and we provide experimental results as proof of concept.

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Discipline of talk: Applied math, deep learning / Advisor: 예종철 (Jong Chul Ye)

For complex number $\alpha$, let $ A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 \\ \alpha & 1 \end{bmatrix} $ be two parabolic matrices and let $G_\alpha$ be the group generated by these two matrices. Determining whether $G_\alpha$ is the free group rank 2 or not, is one of the important problems. In this talk, I will introduce a geometric aspect of the group $G_\alpha$ and give previous results of the problem. Next, I will introduce my work joint with KyeongRo Kim.

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Discipline of talk: Geometric Group Theory / Advisor: 백형렬 교수님