Related papers: Stochastic Normalizing Flows for Inverse Problems:…

For many applications, such as computing the expected value of different magnitudes, sampling from a known probability density function, the target density, is crucial but challenging through the inverse transform. In these cases, rejection…

We present a novel generative modeling method called diffusion normalizing flow based on stochastic differential equations (SDEs). The algorithm consists of two neural SDEs: a forward SDE that gradually adds noise to the data to transform…

We approach the problem of learning continuous normalizing flows from a dual perspective motivated by entropy-regularized optimal transport, in which continuous normalizing flows are cast as gradients of scalar potential functions. This…

In this study, we use Rational-Quadratic Neural Spline Flows, a sophisticated parametrization of Normalizing Flows, for inferring posterior probability distributions in scenarios where direct evaluation of the likelihood is challenging at…

We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model…

This paper investigates an inverse source problem for general semilinear stochastic hyperbolic equations. Motivated by the challenges arising from both randomness and nonlinearity, we develop a globally convergent iterative regularization…

The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows which are families of probability distributions on the space of solutions to the associated ODEs, which no longer satisfy…

Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…

Normalizing flow is a class of deep generative models for efficient sampling and likelihood estimation, which achieves attractive performance, particularly in high dimensions. The flow is often implemented using a sequence of invertible…

A new concept of {\em an evolution system of measures for stochastic flows} is considered. It corresponds to the notion of an invariant measure for random dynamical systems (or cocycles). The existence of evolution systems of measures for…

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…

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…

The purpose of this article is to extend the notion of statistical depth to the case of sample paths of a Markov chain. Initially introduced to define a center-outward ordering of points in the support of a multivariate distribution, depth…

We present a backward diffusion flow (i.e. a backward-in-time stochastic differential equation) whose marginal distribution at any (earlier) time is equal to the smoothing distribution when the terminal state (at a latter time) is…

Normalizing Flows explicitly maximize a full-dimensional likelihood on the training data. However, real data is typically only supported on a lower-dimensional manifold leading the model to expend significant compute on modeling noise.…

Real-world data with underlying structure, such as pictures of faces, are hypothesized to lie on a low-dimensional manifold. This manifold hypothesis has motivated state-of-the-art generative algorithms that learn low-dimensional data…

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…

We consider a Schr\"odinger bridge problem where the Markov process is subject to parameter perturbations, forming an ensemble of systems. Our objective is to steer this ensemble from the initial distribution to the final distribution using…

Normalizing Flows (NFs) are a classical family of likelihood-based methods that have received revived attention. Recent efforts such as TARFlow have shown that NFs are capable of achieving promising performance on image modeling tasks,…

Conditional normalizing flows can generate diverse image samples for solving inverse problems. Most normalizing flows for inverse problems in imaging employ the conditional affine coupling layer that can generate diverse images quickly.…