3 citations · 4 across the 15 of their papers we have counts for
17 papers
Improving score-based sampling via affine post-processing
Curtis McDonald, Kevin Rojas, Molei Tao +1
Sampling from a probability distribution with access only to its log-density is a foundational problem in statistics, machine learning, and the physical sciences. This problem is s…
Diffusion Model's Generalization Can Be Characterized by Inductive Biases toward a Data-Dependent Ridge Manifold
Ye He, Yitong Qiu, Molei Tao
We study a data-dependent notion of diffusion-model generalization: when a model does not memorize the training set, where do its generated samples go relative to the geometry indu…
Fast Non-Log-Concave Sampling under Nonconvex Equality and Inequality Constraints with Landing
Kijung Jeon, Michael Muehlebach, Molei Tao
Sampling from constrained statistical distributions is a fundamental task in various fields including Bayesian statistics, computational chemistry, and statistical physics. This ar…
AlignFlow: Improving Flow-based Generative Models with Semi-Discrete Optimal Transport
Lingkai Kong, Molei Tao, Yang Liu +4
Flow-based Generative Models (FGMs) effectively transform noise into complex data distributions. Incorporating Optimal Transport (OT) to couple noise and data during FGM training h…
Improving Classifier-Free Guidance in Masked Diffusion: Low-Dim Theoretical Insights with High-Dim Impact
Kevin Rojas, Ye He, Chieh-Hsin Lai +3
Classifier-Free Guidance (CFG) is a widely used technique for conditional generation and improving sample quality in continuous diffusion models, and its extensions to discrete dif…
What Exactly Does Guidance Do in Masked Discrete Diffusion Models
He Ye, Rojas Kevin, Tao Molei
We study masked discrete diffusion models with classifier-free guidance (CFG). Assuming no score error nor discretization error, we derive an explicit solution to the guided revers…
Variational Learning Finds Flatter Solutions at the Edge of Stability
Avrajit Ghosh, Bai Cong, Rio Yokota +5
Variational Learning (VL) has recently gained popularity for training deep neural networks. Part of its empirical success can be explained by theories such as PAC-Bayes bounds, min…
Variational Schrödinger Momentum Diffusion
Kevin Rojas, Yixin Tan, Molei Tao +2
The momentum Schrödinger Bridge (mSB) has emerged as a leading method for accelerating generative diffusion processes and reducing transport costs. However, the lack of simulation-…
DeepTTV: Deep Learning Prediction of Hidden Exoplanet From Transit Timing Variations
Chen Chen, Lingkai Kong, Gongjie Li +1
Transit timing variation (TTV) provides rich information about the mass and orbital properties of exoplanets, which are often obtained by solving an inverse problem via Markov Chai…
Quantitative Convergences of Lie Group Momentum Optimizers
Lingkai Kong, Molei Tao
Explicit, momentum-based dynamics that optimize functions defined on Lie groups can be constructed via variational optimization and momentum trivialization. Structure preserving ti…
Quantum State Generation with Structure-Preserving Diffusion Model
Yuchen Zhu, Tianrong Chen, Evangelos A. Theodorou +2
This article considers the generative modeling of the (mixed) states of quantum systems, and an approach based on denoising diffusion model is proposed. The key contribution is an…
Trivialized Momentum Facilitates Diffusion Generative Modeling on Lie Groups
Yuchen Zhu, Tianrong Chen, Lingkai Kong +2
The generative modeling of data on manifolds is an important task, for which diffusion models in flat spaces typically need nontrivial adaptations. This article demonstrates how a…
Convergence of Kinetic Langevin Monte Carlo on Lie groups
Lingkai Kong, Molei Tao
Explicit, momentum-based dynamics for optimizing functions defined on Lie groups was recently constructed, based on techniques such as variational optimization and left trivializat…
Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusion
Ye He, Kevin Rojas, Molei Tao
This paper considers the problem of sampling from non-logconcave distribution, based on queries of its unnormalized density. It first describes a framework, Denoising Diffusion Mon…
DFU: scale-robust diffusion model for zero-shot super-resolution image generation
Alex Havrilla, Kevin Rojas, Wenjing Liao +1
Diffusion generative models have achieved remarkable success in generating images with a fixed resolution. However, existing models have limited ability to generalize to different…
Appropriate State-Dependent Friction Coefficient Accelerates Kinetic Langevin Dynamics
Keunwoo Lim, Molei Tao
We consider the convergence of kinetic Langevin dynamics to its ergodic invariant measure, which is Gibbs distribution. Instead of the standard setup where the friction coefficient…
Mirror Diffusion Models for Constrained and Watermarked Generation
Guan-Horng Liu, Tianrong Chen, Evangelos A. Theodorou +1
Modern successes of diffusion models in learning complex, high-dimensional data distributions are attributed, in part, to their capability to construct diffusion processes with ana…