Diffusion models for high dimensional distributions
报告人： 童心（National University of Singapore）
时间：2025-07-03 14:00-15:00
地点：智华楼四元厅
Abstract:
Diffusion model is a popular tool to generate new data samples. However, rigorous understanding of diffusion model is still lacking.
One issue is how to train these models for high dimensional problems as score function estimation is subject to the curse of dimension.
Another issue is how to avoid the memorization effect, where the diffusion model is bound to generate an exact copy from the training data.
We will provide solutions to the first issue by focusing on high dimensional distributions with sparse dependence. We will leverage the sparse dependence to provide a local estimation of the score functions.
As for the second issue, we will modify the diffusion model in the final stage and generate new samples close to the same manifold where the training data is originated.
About the Speaker:
Xin Tong is an Associate Professor in the Department of Mathematics at the National University of Singapore. He earned his undergraduate degree from Peking University in 2009 and completed his PhD in Operations Research and Financial Engineering at Princeton University. His primary research interests focus on developing theories and methodologies that exploit problem-specific structures in areas such as Uncertainty Quantification, Machine Learning, and Operations Research.
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