Related papers: Turning Normalizing Flows into Monge Maps with Geo…
Stokes inversion techniques are very powerful methods for obtaining information on the thermodynamic and magnetic properties of solar and stellar atmospheres. In recent years, very sophisticated inversion codes have been developed that are…
We propose an algorithm for taming Normalizing Flow models - changing the probability that the model will produce a specific image or image category. We focus on Normalizing Flows because they can calculate the exact generation probability…
We introduce stochastic normalizing flows, an extension of continuous normalizing flows for maximum likelihood estimation and variational inference (VI) using stochastic differential equations (SDEs). Using the theory of rough paths, the…
We introduce and analyze a statistical estimator for Monge transport maps: solutions to the quadratic optimal transport problem in Euclidean space. For absolutely continuous source measures, this map is uniquely defined as the gradient of a…
Normalising flows are tractable probabilistic models that leverage the power of deep learning to describe a wide parametric family of distributions, all while remaining trainable using maximum likelihood. We discuss how these methods can be…
We investigate the use of normalizing flow (NF) models as flexible priors in Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling for iterative Bayesian calibration. Trained on posteriors from previous analyses, these models can…
Efficient gradient computation of the Jacobian determinant term is a core problem in many machine learning settings, and especially so in the normalizing flow framework. Most proposed flow models therefore either restrict to a function…
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…
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…
Our universe is homogeneous and isotropic, and its perturbations obey translation and rotation symmetry. In this work we develop Translation and Rotation Equivariant Normalizing Flow (TRENF), a generative Normalizing Flow (NF) model which…
We study the geometry of conditional optimal transport (COT) and prove a dynamical formulation which generalizes the Benamou-Brenier Theorem. Equipped with these tools, we propose a simulation-free flow-based method for conditional…
Estimating optimal transport (OT) maps (a.k.a. Monge maps) between two measures $P$ and $Q$ is a problem fraught with computational and statistical challenges. A promising approach lies in using the dual potential functions obtained when…
Normalizing flows are a powerful tool to create flexible probability distributions with a wide range of potential applications in cosmology. Here we are studying normalizing flows which represent cosmological observables at field level,…
General-purpose Markov Chain Monte Carlo sampling algorithms suffer from a dramatic reduction in efficiency as the system being studied is driven towards a critical point. Recently, a series of seminal studies suggested that normalizing…
Normalizing flows and variational autoencoders are powerful generative models that can represent complicated density functions. However, they both impose constraints on the models: Normalizing flows use bijective transformations to model…
Flow-based models are powerful tools for designing probabilistic models with tractable density. This paper introduces Convex Potential Flows (CP-Flow), a natural and efficient parameterization of invertible models inspired by the optimal…
In this paper, we propose normalizing flows (NF) as a novel probability density function (PDF) turbulence model (NF-PDF model) for the Reynolds-averaged Navier-Stokes (RANS) equations. We propose to use normalizing flows in two different…
In this work, we propose the Generative Latent Flow (GLF), an algorithm for generative modeling of the data distribution. GLF uses an Auto-encoder (AE) to learn latent representations of the data, and a normalizing flow to map the…
Normalizing flows are objects used for modeling complicated probability density functions, and have attracted considerable interest in recent years. Many flexible families of normalizing flows have been developed. However, the focus to date…
Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…