Related papers: Lipschitz-regularized gradient flows and generativ…

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…

Generative networks are opening new avenues in fast event generation for the LHC. We show how generative flow networks can reach percent-level precision for kinematic distributions, how they can be trained jointly with a discriminator, and…

This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…

Generative Flow Networks (GFlowNets) are amortized inference models designed to sample from unnormalized distributions over composable objects, with applications in generative modeling for tasks in fields such as causal discovery, NLP, and…

Score-based generative models (SGMs) aim at estimating a target data distribution by learning score functions using only noise-perturbed samples from the target.Recent literature has focused extensively on assessing the error between the…

Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…

Learning to sample from intractable distributions over discrete sets without relying on corresponding training data is a central problem in a wide range of fields, including Combinatorial Optimization. Currently, popular deep learning-based…

High-dimensional generative modeling is fundamentally a manifold-learning problem: real data concentrate near a low-dimensional structure embedded in the ambient space. Effective generators must therefore balance support fidelity -- placing…

We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…

Sampling from high-dimensional and structured probability distributions is a fundamental challenge in computational physics, particularly in the context of lattice field theory (LFT), where generating field configurations efficiently is…

Under general assumptions on the target distribution $p^\star$, we establish a sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores, with optimal dependence on time and dimension. As applications, we…

In this paper, we propose a distributed first-order algorithm with backtracking linesearch for solving multi-agent minimisation problems, where each agent handles a local objective involving nonsmooth and smooth components. Unlike existing…

Flow Matching, a promising approach in generative modeling, has recently gained popularity. Relying on ordinary differential equations, it offers a simple and flexible alternative to diffusion models, which are currently the…

Training generative models to sample from unnormalized density functions is an important and challenging task in machine learning. Traditional training methods often rely on the reverse Kullback-Leibler (KL) divergence due to its…

Flow-based generative models have demonstrated promising performance across a broad spectrum of data modalities (e.g., image and text). However, there are few works exploring their extension to unordered data (e.g., spatial point set),…

We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…

We propose the characteristic generator, a novel one-step generative model that combines the efficiency of sampling in Generative Adversarial Networks (GANs) with the stable performance of flow-based models. Our model is driven by…

We propose a novel diffusion map particle system (DMPS) for generative modeling, based on diffusion maps and Laplacian-adjusted Wasserstein gradient descent (LAWGD). Diffusion maps are used to approximate the generator of the corresponding…

We introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on…

Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…