Ye He (何晔)

Mathematical foundations of generative AI, sampling, and generalization.

I am an Assistant Professor in the Department of Applied Mathematics at the University of Colorado Boulder.

My research studies the mathematical foundations of artificial intelligence and machine learning, with a particular interest in the mechanisms underlying generative models, sampling and inference, and generalization. I aim to understand how the structure of data and learning algorithms gives rise to effective representations, inductive biases, and scalable computational methods.

Previously, I was a Hale Visiting Assistant Professor in the School of Mathematics at the Georgia Institute of Technology, hosted by Prof. Molei Tao . I received my Ph.D. in Mathematics from the University of California, Davis, advised by Prof. Krishna Balasubramanian .

I am currently looking for Ph.D. students interested in generative modeling, sampling, generalization, and the mathematical foundations of machine learning.

Download CV Research Publications

Research

Mathematical foundations of modern machine learning, generative modeling, and inference.

My research broadly aims to characterize the mechanisms behind modern learning and inference methods, with an emphasis on the interaction between data structure, algorithmic dynamics, generalization, and computation.

Generative Models and Diffusion

I study the mathematical mechanisms underlying diffusion and related generative models, including generalization, classifier-free guidance, learned score functions, posterior structure, and data-dependent geometry.

Sampling and Inference

I develop and analyze scalable sampling and inference methods for complex distributions, including non-log-concave and heavy-tailed targets, particle-based methods, Langevin-type algorithms, and diffusion-based approaches.

Generalization and Inductive Bias

I study how structural properties of data and learning algorithms shape generalization, representation, and emergent geometric behavior in modern machine-learning models.

Publications

Papers in generative modeling, sampling, optimization, and the mathematical foundations of machine learning.

Diffusion Model's Generalization Can Be Characterized by Inductive Biases toward a Data-Dependent Ridge Manifold

Ye He, Yitong Qiu, and Molei Tao (2026).

Preprint. Link
Finite-Particle Rates for Regularized Stein Variational Gradient Descent

Ye He, Krishnakumar Balasubramanian, Sayan Banerjee, and Promit Ghosal (2026).

Preprint. Link
Theory-Informed Improvements to Classifier-Free Guidance for Discrete Diffusion Models

Kevin Rojas, Ye He, Chieh-Hsin Lai, Yuta Takida, Yuki Mitsufuji, and Molei Tao (2025).

ICLR 2026. Link
What Exactly Does Guidance Do in Masked Discrete Diffusion Models

Ye He, Kevin Rojas, and Molei Tao (2025).

ICLR 2026. Link
Evaluating the Design Space of Diffusion-based Generative Models

Yuqing Wang, Ye He, and Molei Tao (2024).

NeurIPS 2024. Link
A Separation in Heavy-tailed Sampling: Gaussian vs. Stable Oracles for Proximal Samplers

Ye He, Alireza Mousavi-Hosseini, Krishnakumar Balasubramanian, and Murat A. Erdogdu (2024).

NeurIPS 2024. Link
Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusion

Ye He, Kevin Rojas, and Molei Tao (2024).

NeurIPS 2024. Link
High-dimensional Scaling Limits and Fluctuations of Online Least-Squares SGD with Smooth Covariance

Krishnakumar Balasubramanian, Promit Ghosal, and Ye He (2024, authors listed alphabetically).

Annals of Applied Probability. Link
Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincaré Inequality

Alireza Mousavi-Hosseini, Tyler K. Farghly, Ye He, Krishnakumar Balasubramanian, and Murat A. Erdogdu (2023).

COLT 2023. Link
An Analysis of Transformed Unadjusted Langevin Algorithm for Heavy-tailed Sampling

Ye He, Krishnakumar Balasubramanian, and Murat A. Erdogdu (2022).

IEEE Transactions on Information Theory. Link
Regularized Stein Variational Gradient Flow

Ye He, Krishnakumar Balasubramanian, Bharath K. Sriperumbudur, and Jianfeng Lu (2022).

Foundations of Computational Mathematics. Link
Mean-Square Analysis of Discretized Itô Diffusions for Heavy-Tailed Sampling

Ye He, Tyler K. Farghly, Krishnakumar Balasubramanian, and Murat A. Erdogdu (2022).

Journal of Machine Learning Research. Link
On the Ergodicity, Bias and Asymptotic Normality of Randomized Midpoint Sampling Method

Ye He, Krishnakumar Balasubramanian, and Murat A. Erdogdu (2020).

NeurIPS 2020. Link