相关论文: Sampling Boltzmann distributions via normalizing f…
Normalizing flows are flexible, parameterized distributions that can be used to approximate expectations from intractable distributions via importance sampling. However, current flow-based approaches are limited on challenging targets where…
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…
Normalizing Flows (NF) are powerful likelihood-based generative models that are able to trade off between expressivity and tractability to model complex densities. A now well established research avenue leverages optimal transport (OT) and…
Molecules are frequently represented as graphs, but the underlying 3D molecular geometry (the locations of the atoms) ultimately determines most molecular properties. However, most molecules are not static and at room temperature adopt a…
We present a novel theoretical framework for understanding the expressive power of normalizing flows. Despite their prevalence in scientific applications, a comprehensive understanding of flows remains elusive due to their restricted…
Normalizing flows (NF) are a class of powerful generative models that have gained popularity in recent years due to their ability to model complex distributions with high flexibility and expressiveness. In this work, we introduce a new type…
Many normalizing flow architectures impose regularity constraints, yet their distributional approximation properties are not fully characterized. We study the expressivity of bi-Lipschitz normalizing flows through the lens of score-based…
In this paper, we consider the problem of recovering the $W_2$-optimal transport map T between absolutely continuous measures $\mu,\nu\in\mathcal{P}(\mathbb{R}^n)$ as the flow of a linear-control neural ODE, where the control depends only…
We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plug-in rules that simply replace the true distributions by their empirical…
The Boltzmann machine provides a useful framework to learn highly complex, multimodal and multiscale data distributions that occur in the real world. The default method to learn its parameters consists of minimizing the Kullback-Leibler…
The generation of equilibrium samples of molecular systems has been a long-standing problem in statistical physics. Boltzmann Generators are a generative machine learning method that addresses this issue by learning a transformation via a…
The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo…
In many applications in statistics and machine learning, the availability of data samples from multiple possibly heterogeneous sources has become increasingly prevalent. On the other hand, in distributionally robust optimization, we seek…
We present a computational framework for efficient learning, sampling, and distribution of general Bayesian posterior distributions. The framework leverages a machine learning approach for the construction of normalizing flows for the…
Normalizing flows (NF) use a continuous generator to map a simple latent (e.g. Gaussian) distribution, towards an empirical target distribution associated with a training data set. Once trained by minimizing a variational objective, the…
Scalable sampling of molecular states in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann Generators tackle this problem by pairing a generative model, capable of exact likelihood computation, with…
Flows are exact-likelihood generative neural networks that transform samples from a simple prior distribution to the samples of the probability distribution of interest. Boltzmann Generators (BG) combine flows and statistical mechanics to…
In this paper, we suggest a novel sampling method for Monte Carlo molecular simulations. In order to perform efficient sampling of molecular systems, it is advantageous to avoid extremely high energy configurations while also retaining the…
We propose a novel method for sampling from unnormalized Boltzmann densities based on a probability flow ordinary differential equation (ODE) derived from linear stochastic interpolants. The key innovation of our approach is the use of a…
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…