Related papers: The Wasserstein Proximal Gradient Algorithm

We propose a variational scheme for computing Wasserstein gradient flows. The scheme builds upon the Jordan--Kinderlehrer--Otto framework with the Benamou-Brenier's dynamic formulation of the quadratic Wasserstein metric and adds a…

Particle-based variational inference methods (ParVIs) such as Stein variational gradient descent (SVGD) update the particles based on the kernelized Wasserstein gradient flow for the Kullback-Leibler (KL) divergence. However, the design of…

Score-based diffusion models currently constitute the state of the art in continuous generative modeling. These methods are typically formulated via overdamped or underdamped Ornstein--Uhlenbeck-type stochastic differential equations, in…

We investigate proximal descent methods, inspired by the minimizing movement scheme introduced by Jordan, Kinderlehrer and Otto, for optimizing entropy-regularized functionals on the Wasserstein space. We establish linear convergence under…

This paper presents a new approach to the classical problem of quantifying posterior contraction rates (PCRs) in Bayesian statistics. Our approach relies on Wasserstein distance, and it leads to two main contributions which improve on the…

We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced…

Developing machine learning methods that are privacy preserving is today a central topic of research, with huge practical impacts. Among the numerous ways to address privacy-preserving learning, we here take the perspective of computing the…

As the demand to integrate Artificial Intelligence into high-stakes environments continues to grow, explaining the reasoning behind neural-network predictions has shifted from a theoretical curiosity to a strict operational requirement. Our…

Performativity means that the deployment of a predictive model incentivizes agents to strategically adapt their behavior, thereby inducing a model-dependent distribution shift. Practitioners often repeatedly retrain the model on data…

Existing analyses of optimization in deep learning are either continuous, focusing on (variants of) gradient flow, or discrete, directly treating (variants of) gradient descent. Gradient flow is amenable to theoretical analysis, but is…

Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by…

Generative modeling typically concerns transporting a single source distribution to a target distribution via simple probability flows. However, in fields like computer graphics and single-cell genomics, samples themselves can be viewed as…

Flow Matching has become a cornerstone of modern generative models like Stable Diffusion 3, largely due to the efficiency of its Rectified Flow (RF) variant. The success of RF hinges on iteratively learning straight trajectories, pushing…

Projection robust Wasserstein (PRW) distance, or Wasserstein projection pursuit (WPP), is a robust variant of the Wasserstein distance. Recent work suggests that this quantity is more robust than the standard Wasserstein distance, in…

Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…

In this paper we propose two proximal gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either…

Vision-Language Latent Diffusion Models (LDMs) (Rombach et al., 2022) provide powerful generative priors for inverse problems. However, existing LDM-based inverse solvers typically require a large number of neural function evaluations…

We study the minimization of non-convex functionals over the Wasserstein space. While recent work has showed that perturbed Wasserstein gradient methods can avoid saddle points for benign landscapes, existing approaches remain essentially…

In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. While this approach also controls the distance between the posterior…

We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein distance of order $2$. Our result holds as long as the…