Related papers: On the Wasserstein Gradient Flow Interpretation of…

Generative flow networks (GFNs) are a class of models for sequential sampling of composite objects, which approximate a target distribution that is defined in terms of an energy function or a reward. GFNs are typically trained using a flow…

Wasserstein gradient flows provide a powerful means of understanding and solving many diffusion equations. Specifically, Fokker-Planck equations, which model the diffusion of probability measures, can be understood as gradient descent over…

Sliced-Wasserstein Flow (SWF) is a promising approach to nonparametric generative modeling but has not been widely adopted due to its suboptimal generative quality and lack of conditional modeling capabilities. In this work, we make two…

We propose kernel-gradient drifting, a one-step generative modeling framework that replaces the fixed Euclidean displacement direction in drifting models with directions induced by the kernel itself. Standard drifting is attractive because…

We propose a novel particle-based variational inference method designed to work with multimodal distributions. Our approach, referred to as Branched Stein Variational Gradient Descent (BSVGD), extends the classical Stein Variational…

Geometric data and purpose-built generative models on them have become ubiquitous in high-impact deep learning application domains, ranging from protein backbone generation and computational chemistry to geospatial data. Current geometric…

We study the Wasserstein gradient flow of the Sinkhorn divergence when both the source and the target are Gaussian distributions. We prove the existence of a flow that stays in the class of Gaussian distributions, and is unique in the…

In many domains of computer vision, generative adversarial networks (GANs) have achieved great success, among which the family of Wasserstein GANs (WGANs) is considered to be state-of-the-art due to the theoretical contributions and…

This paper develops a generative model by minimizing the second-order Wasserstein loss (the $W_2$ loss) through a distribution-dependent ordinary differential equation (ODE), whose dynamics involves the Kantorovich potential associated with…

We introduce Midpoint Generative Models (MGM), a principled framework for training one-step generative models. MGM is based on a simple symmetry of Flow Matching with linear interpolation: when the two endpoint distributions coincide, the…

This paper presents a groundbreaking approach to causal inference by integrating continuous normalizing flows (CNFs) with parametric submodels, enhancing their geometric sensitivity and improving upon traditional Targeted Maximum Likelihood…

We introduce the Gaussian transform (GT), an optimal transport inspired iterative method for denoising and enhancing latent structures in datasets. Under the hood, GT generates a new distance function (GT distance) on a given dataset by…

This paper studies minimax optimization problems defined over infinite-dimensional function classes of overparameterized two-layer neural networks. In particular, we consider the minimax optimization problem stemming from estimating linear…

Optimization problem, which is aimed at finding the global minimal value of a given cost function, is one of the central problem in science and engineering. Various numerical methods have been proposed to solve this problem, among which the…

Stein variational gradient descent (SVGD) is a kernel-based and non-parametric particle method for sampling from a target distribution, such as in Bayesian inference and other machine learning tasks. Different from other particle methods,…

Wasserstein gradient flows on probability measures have found a host of applications in various optimization problems. They typically arise as the continuum limit of exchangeable particle systems evolving by some mean-field interaction…

Robots often rely on a repertoire of previously-learned motion policies for performing tasks of diverse complexities. When facing unseen task conditions or when new task requirements arise, robots must adapt their motion policies…

Minimum distance estimation (MDE) gained recent attention as a formulation of (implicit) generative modeling. It considers minimizing, over model parameters, a statistical distance between the empirical data distribution and the model. This…

Diffusion models (DMs) have gained attention in Missing Data Imputation (MDI), but there remain two long-neglected issues to be addressed: (1). Inaccurate Imputation, which arises from inherently sample-diversification-pursuing generative…

Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different…