My current research interests lie at the intersection of stochastic processes and differential geometry. My current directions include (1) understanding and improving diffusion models under the data manifold hypothesis, and (2) understanding the implicit minima-selection phenomenon and improving active minima-selection strategies in nonconvex optimization.

In addition, I am interested in various machine learning topics, including the efficient training of large-scale machine learning models, neural network-based numerical PDE solvers, trustworthy machine learning, and statistical perspectives on machine learning.