105 citations · 125 across the 35 of their papers we have counts for
7 papers · 1 filter
On the Regularity and Generalization of One-Step Wasserstein-guided Generative Models for PDE-Induced Measures
Likun Lin, Zhongjian Wang, Jack Xin +1
Despite the remarkable empirical success of generative models, the available theory on their statistical accuracy in scientific computing remains largely pessimistic. This paper de…
DC-LA: Difference-of-Convex Langevin Algorithm
Hoang Phuc Hau Luu, Zhongjian Wang
We study a sampling problem whose target distribution is where the data fidelity term is Lipschitz smooth while the regularizer term is a non-…
Pathway to Complexity bound under Wasserstein metric of flow-based models
Xiangjun Meng, Zhongjian Wang
We provide attainable analytical tools to estimate the error of flow-based generative models under the Wasserstein metric and to establish the optimal sampling iteration complexity…
COFM: Consistent Optimal Transport Flow Matching via Partially Input Convex Neural Networks
Fanghui Song, Zhongjian Wang, Jiebao Sun
Optimal transport (OT) provides a principled framework for learning mappings between probability distributions, and has found broad applications in generative modeling, inverse pro…
Global Well-posedness and Convergence Analysis of Score-based Generative Models via Sharp Lipschitz Estimates
Connor Mooney, Zhongjian Wang, Jack Xin +1
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…
Mathematical analysis of singularities in the diffusion model under the submanifold assumption
Yubin Lu, Zhongjian Wang, Guillaume Bal
This paper concerns the mathematical analyses of the diffusion model in machine learning. The drift term of the backward sampling process is represented as a conditional expectatio…
DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method
Zhongjian Wang, Jack Xin, Zhiwen Zhang
We introduce the so called DeepParticle method to learn and generate invariant measures of stochastic dynamical systems with physical parameters based on data computed from an inte…