相关论文: Triangular Flows for Generative Modeling: Statisti…
A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the…
Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only…
We study the problem of characterizing the stability of Kullback-Leibler (KL) divergence under Gaussian perturbations beyond Gaussian families. Existing relaxed triangle inequalities for KL divergence critically rely on the assumption that…
The dynamics of gradient and Hamiltonian flows with particular application to flows on adjoint orbits of a Lie group and the extension of this setting to flows on a loop group are discussed. Different types of gradient flows that arise from…
This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…
Simulation-free training frameworks have been at the forefront of the generative modelling revolution in continuous spaces, leading to large-scale diffusion and flow matching models. However, such modern generative models suffer from…
Normalizing Flows provide a principled framework for high-dimensional density estimation and generative modeling by constructing invertible transformations with tractable Jacobian determinants. We propose Fractal Flow, a novel normalizing…
We derive a deterministic, non-asymptotic upper bound on the Kullback-Leibler (KL) divergence of the flow-matching distribution approximation. In particular, if the $L_2$ flow-matching loss is bounded by $\epsilon^2 > 0$, then the KL…
Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions whose support have a complex topological structure, such as…
Multi-phase flows encountered in nature or in industry, exhibit non trivial rheological properties, that can be understood better thanks to model materials and appropriate rheometers. Here, we use model unsaturated granular materials:…
Sampling equilibrium distributions is fundamental to statistical mechanics. While flow matching has emerged as scalable state-of-the-art paradigm for generative modeling, its potential for equilibrium sampling in condensed-phase systems…
We present a generative model that is defined on finite sets of exchangeable, potentially high dimensional, data. As the architecture is an extension of RealNVPs, it inherits all its favorable properties, such as being invertible and…
Normalizing Flows (NFs) are emerging as a powerful class of generative models, as they not only allow for efficient sampling, but also deliver, by construction, density estimation. They are of great potential usage in High Energy Physics…
Recently, flow-based generative models have shown superior efficiency compared to diffusion models. In this paper, we study rectified flow models, which constrain transport trajectories to be linear from the base distribution to the data…
This article presents numerical investigations on accuracy and convergence properties of several numerical approaches for simulating steady state flows in heterogeneous aquifers. Finite difference, finite element, discontinuous Galerkin,…
Recent advances in variational inference enable the modelling of highly structured joint distributions, but are limited in their capacity to scale to the high-dimensional setting of stochastic neural networks. This limitation motivates a…
In the present paper, recent experimental results on large scale coherent steady states observed in experimental von K{\'a}rm{\'a}n flows are revisited from a statistical mechanics perspective. The latter is rooted on two levels of…
Inspired by work of Besson-Courtois-Gallot, we construct a flow called the natural flow on a non-positively curved Riemannian manifold $M$. As with the natural map, the $k$-Jacobian of the natural flow is directly related to the critical…
Through examples of coordinate and probability transformation between different distributions, the basic principle of normalizing flow is introduced in a simple and concise manner. From the perspective of the distribution of random variable…
In this study, we focus on the modelling of coupled systems of shallow water flows and solute transport with source terms due to variable topography and friction effect. Our aim is to propose efficient and accurate numerical techniques for…