2024年06月18日 星期二 登录 EN

学术活动
Global well posedness of Score-Based Generative model via Sharp Lipschitz estimate
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报告人:
Zhongjian Wang, Professor, Nanyang Technological University, Singapore
邀请人:
Tao Zhou, Professor
题目:
Global well posedness of Score-Based Generative model via Sharp Lipschitz estimate
时间地点:
10:00-11:00 June 3 (Monday), N733
摘要:

We establish global well-posedness and convergence of the score-based generative models (SGM) under minimal general assumptions of initial data for score estimation. For the smooth case, we start from a Lipschitz bound of the score function with optimal time length. The optimality is validated by an example whose Lipschitz constant of scores is bounded at initial but blows up in finite time. This necessitates the separation of time scales in conventional bounds for non-log-concave distributions. In contrast, our follow up analysis only relies on a local Lipschitz condition and is valid globally in time. This leads to the convergence of numerical scheme without time separation. For the non-smooth case, we show that the optimal Lipschitz bound is $O(1/t)$ in the point-wise sense for distributions supported on a compact, smooth and low-dimensional manifold with boundary.