Related papers: OT-Flow: Fast and Accurate Continuous Normalizing …

Conditional Normalizing Flows (CNFs) are flexible generative models capable of representing complicated distributions with high dimensionality and large interdimensional correlations, making them appealing for structured output learning.…

We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…

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…

This paper investigates the semi-discrete optimal transport (OT) problem with entropic regularization. We characterize the solution using a governing, well-posed ordinary differential equation (ODE). This naturally yields an algorithm to…

Despite notable successes of Reinforcement Learning (RL), the prevalent use of an online learning paradigm prevents its widespread adoption, especially in hazardous or costly scenarios. Offline RL has emerged as an alternative solution,…

Neural ordinary differential equations (ODEs) provide expressive representations of invertible transport maps that can be used to approximate complex probability distributions, e.g., for generative modeling, density estimation, and Bayesian…

Optimal Transport (OT) has established itself as a robust framework for quantifying differences between distributions, with applications that span fields such as machine learning, data science, and computer vision. This paper offers a…

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate…

Flow models have rapidly become the go-to method for training and deploying large-scale generators, owing their success to inference-time flexibility via adjustable integration steps. A crucial ingredient in flow training is the choice of…

We study the estimation of optimal transport (OT) maps between an arbitrary source probability measure and a log-concave target probability measure. Our contributions are twofold. First, we propose a new evolution equation in the set of…

Normalizing Flows (NFs) are widely used in deep generative models for their exact likelihood estimation and efficient sampling. However, they require substantial memory since the latent space matches the input dimension. Multi-scale…

Normalizing Flows are generative models that directly maximize the likelihood. Previously, the design of normalizing flows was largely constrained by the need for analytical invertibility. We overcome this constraint by a training procedure…

We reformulate Optimal Transport Conditional Flow Matching (OT-CFM), a class of dynamical generative models, showing that it admits an exact proximal formulation via an extended Brenier potential, without assuming that the target…

Optimal Transport (OT) theory has seen an increasing amount of attention from the computer science community due to its potency and relevance in modeling and machine learning. It introduces means that serve as powerful ways to compare…

Flow models parameterized as time-dependent velocity fields can generate data from noise by integrating an ODE. These models are often trained using flow matching, i.e. by sampling random pairs of noise and target points…

Predicting potential and counterfactual outcomes from observational data is central to individualized decision-making, particularly in clinical settings where treatment choices must be tailored to each patient rather than guided solely by…

Rectified flow is a generative model that learns smooth transport mappings between two distributions through an ordinary differential equation (ODE). Unlike diffusion-based generative models, which require costly numerical integration of a…

Two fundamental problems in unsupervised learning are efficient inference for latent-variable models and robust density estimation based on large amounts of unlabeled data. Algorithms for the two tasks, such as normalizing flows and…

Normalizing Flows (NFs) have been established as a principled framework for generative modeling. Standard NFs consist of a forward process and a reverse process: the forward process maps data to noise, while the reverse process generates…

Normalizing flows define a probability distribution by an explicit invertible transformation $\boldsymbol{\mathbf{z}}=f(\boldsymbol{\mathbf{x}})$. In this work, we present implicit normalizing flows (ImpFlows), which generalize normalizing…