Huibin Zhou
Yale University, CT·Mathematics & Statistics
Generative artificial intelligence systems that produce images and text work impressively well, but there is little mathematical theory explaining why. At their core, these systems solve a high-dimensional density estimation problem: learning the shape of a complicated probability distribution from samples.
- Fields
Mathematics & Statistics
Computer Science
- Topics
generative models
diffusion models
rectified flow
- Grants
- 1 known grant, through Jul 2027
What they work on
- Determine whether the iterative rectified flow algorithm, which turns high-dimensional density estimation into repeated regression, achieves optimal density and transport estimation in just one step of regression.
- Quantify how fast the iterative regression of rectified flow converges to the optimal transport map, the most efficient way of morphing a simple noise distribution into a complex data distribution.
- Propose an improved algorithm over rectified flow with better statistical and computational guarantees, and establish guarantees for score-based diffusion models.
- Improve denoising diffusion probabilistic models with an iterative algorithm that attains the optimal transport, using connections through score matching, ordinary and stochastic differential equations, and nonparametric empirical Bayes.
- Explore applications of generative models and optimal transport to neuroscience data and autism spectrum disorder.
More about the research
They can equally be seen as a transport problem, gradually turning simple random noise into a realistic image or sentence. Without statistical guarantees, it is hard to say how much data or computation an algorithm truly needs, and current training is slow and energy-hungry. This project builds the theory.
Why it matters
Generative AI is deployed widely without theory that says when its output can be trusted or how much computation it really requires, and training these models consumes large amounts of energy. Statistical and computational guarantees for rectified flow and diffusion models could justify faster, less energy-intensive algorithms and guide the design of improved ones. Applications to neuroscience data and autism spectrum disorder are also explored.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Yusu Wang
University of California-San Diego, CA·Computer Science
Explain why trained flow-based and diffusion generative models generalize better than the theoretically optimal solution predicts, using geometry, ODE analysis, manifold learning and deep learning theory, to enable controlled generation of novel samples.
Yongxin Chen
Georgia Institute of Technology, GA·Engineering
Develop theory and algorithms for controlling probability distributions of agents whose dynamics are nonlinear in state and non-affine in control, with optimality guarantees under hard deadlines.
Haomin Zhou
Georgia Institute of Technology, GA·Mathematics & Statistics
Establish parameterized Wasserstein sub-manifolds, which represent evolving probability distributions through a neural network's parameters via a push-forward map and pullback metric, and develop their mathematical foundations.
The school
Yale University: 73 labs on PI Pages, $1.5B a year on research, 438 research doctorates a year.
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