Related papers: Generative Modeling by Minimizing the Wasserstein-…

Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…

Learning probabilistic models that can estimate the density of a given set of samples, and generate samples from that density, is one of the fundamental challenges in unsupervised machine learning. We introduce a new generative model based…

Discrete diffusion models have emerged as a powerful paradigm for generative modeling on sequence data; however, the information-theoretic principles governing their reverse processes remain significantly less understood than those of their…

Diffusion models are one of the most important families of deep generative models. In this note, we derive a quantitative upper bound on the Wasserstein distance between the data-generating distribution and the distribution learned by a…

Unconstrained Online Linear Optimization (OLO) is a practical problem setting to study the training of machine learning models. Existing works proposed a number of potential-based algorithms, but in general the design of these potential…

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…

We propose a novel second-order ODE as the continuous-time limit of a Riemannian accelerated gradient-based method on a manifold with curvature bounded from below. This ODE can be seen as a generalization of the ODE derived for Euclidean…

The population dynamics of molecules, cells, and organisms are governed by a number of unknown forces. In the last decade, population dynamics have predominantly been modeled with Wasserstein gradient flows. However, since gradient flows…

The sliced Wasserstein flow (SWF), a nonparametric and implicit generative gradient flow, is transformed into a Liouville partial differential equation (PDE)-based formalism. First, the stochastic diffusive term from the Fokker-Planck…

Gradient boosting is a sequential ensemble method that fits a new weaker learner to pseudo residuals at each iteration. We propose Wasserstein gradient boosting, a novel extension of gradient boosting that fits a new weak learner to…

Score-based diffusion models have become a foundational paradigm for modern generative modeling, demonstrating exceptional capability in generating samples from complex high-dimensional distributions. Despite the dominant adoption of…

Wasserstein Barycenter is a principled approach to represent the weighted mean of a given set of probability distributions, utilizing the geometry induced by optimal transport. In this work, we present a novel scalable algorithm to…

Optimal Transport (OT) has attracted significant interest in the machine learning community, not only for its ability to define meaningful distances between probability distributions -- such as the Wasserstein distance -- but also for its…

Wasserstein distributionally robust optimization (DRO) aims to find robust and generalizable solutions by hedging against data perturbations in Wasserstein distance. Despite its recent empirical success in operations research and machine…

A nonlinear diffusion equation, interpreted as a Wasserstein gradient flow, is numerically solved in one space dimension using a higher-order minimizing movement scheme based on the BDF (backward differentiation formula) discretization. In…

We develop novel neural network-based implicit particle methods to compute high-dimensional Wasserstein-type gradient flows with linear and nonlinear mobility functions. The main idea is to use the Lagrangian formulation in the…

Deep generative models aim to learn underlying distributions that generate the observed data. Given the fact that the generative distribution may be complex and intractable, deep latent variable models use probabilistic frameworks to learn…

We study distributionally robust optimization (DRO) problems where the ambiguity set is defined using the Wasserstein metric. We show that this class of DRO problems can be reformulated as semi-infinite programs. We give an exchange method…

In this work, we propose a novel generalized Wasserstein-2 distance approach for efficiently training stochastic neural networks to reconstruct random field models, where the target random variable comprises both continuous and categorical…

We study the Wasserstein gradient flow of semi-discrete energies in the space of probability measures, that is functionals depending on two measures-one being an absolutely continuous density and the other an atomic measure. These energies…