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Normalizing Flows (NFs) are a class of generative models distinguished by a mathematically invertible architecture, where the forward pass transforms data into a latent space for density estimation, and the reverse pass generates new…

Computer Vision and Pattern Recognition · Computer Science 2025-12-05 Yang Chen , Xiaowei Xu , Shuai Wang , Chenhui Zhu , Ruxue Wen , Xubin Li , Tiezheng Ge , Limin Wang

Normalizing Flows (NFs) describe a class of models that express a complex target distribution as the composition of a series of bijective transformations over a simpler base distribution. By limiting the space of candidate transformations…

Machine Learning · Computer Science 2023-09-11 Keegan Kelly , Lorena Piedras , Sukrit Rao , David Roth

Normalizing Flows (NFs) are likelihood-based models for continuous inputs. They have demonstrated promising results on both density estimation and generative modeling tasks, but have received relatively little attention in recent years. In…

Computer Vision and Pattern Recognition · Computer Science 2025-06-09 Shuangfei Zhai , Ruixiang Zhang , Preetum Nakkiran , David Berthelot , Jiatao Gu , Huangjie Zheng , Tianrong Chen , Miguel Angel Bautista , Navdeep Jaitly , Josh Susskind

The Normalizing Flow (NF) models a general probability density by estimating an invertible transformation applied on samples drawn from a known distribution. We introduce a new type of NF, called Deep Diffeomorphic Normalizing Flow (DDNF).…

Machine Learning · Statistics 2018-11-26 Hadi Salman , Payman Yadollahpour , Tom Fletcher , Kayhan Batmanghelich

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…

Machine Learning · Statistics 2023-03-01 Humberto Reyes-Gonzalez , Riccardo Torre

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…

Machine Learning · Computer Science 2024-04-25 Felix Draxler , Peter Sorrenson , Lea Zimmermann , Armand Rousselot , Ullrich Köthe

Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of…

Machine Learning · Computer Science 2023-11-14 Christina Winkler , Daniel Worrall , Emiel Hoogeboom , Max Welling

Normalizing Flows (NFs) are flexible explicit generative models that have been shown to accurately model complex real-world data distributions. However, their invertibility constraint imposes limitations on data distributions that reside on…

Computer Vision and Pattern Recognition · Computer Science 2022-08-19 Janis Postels , Martin Danelljan , Luc Van Gool , Federico Tombari

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,…

Computer Vision and Pattern Recognition · Computer Science 2026-04-23 Tianrong Chen , Jiatao Gu , David Berthelot , Joshua Susskind , Shuangfei Zhai

By chaining a sequence of differentiable invertible transformations, normalizing flows (NF) provide an expressive method of posterior approximation, exact density evaluation, and sampling. The trend in normalizing flow literature has been…

Machine Learning · Computer Science 2020-10-20 Robert Giaquinto , Arindam Banerjee

Modern reinforcement learning (RL) algorithms have found success by using powerful probabilistic models, such as transformers, energy-based models, and diffusion/flow-based models. To this end, RL researchers often choose to pay the price…

Machine Learning · Computer Science 2025-06-05 Raj Ghugare , Benjamin Eysenbach

Normalizing Flows (NFs) learn invertible mappings between the data and a Gaussian distribution. Prior works usually suffer from two limitations. First, they add random noise to training samples or VAE latents as data augmentation,…

Computer Vision and Pattern Recognition · Computer Science 2025-12-04 Qinyu Zhao , Guangting Zheng , Tao Yang , Rui Zhu , Xingjian Leng , Stephen Gould , Liang Zheng

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…

Machine Learning · Statistics 2020-10-27 Hao Wu , Jonas Köhler , Frank Noé

Normalizing flows (NFs) have become a prominent method for deep generative models that allow for an analytic probability density estimation and efficient synthesis. However, a flow-based network is considered to be inefficient in parameter…

Machine Learning · Computer Science 2020-10-26 Sang-gil Lee , Sungwon Kim , Sungroh Yoon

Normalizing Flows (NF) are Generative models which transform a simple prior distribution into the desired target. They however require the design of an invertible mapping whose Jacobian determinant has to be computable. Recently introduced,…

Machine Learning · Computer Science 2025-09-18 Vincent Souveton , Arnaud Guillin , Jens Jasche , Guilhem Lavaux , Manon Michel

Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…

Machine Learning · Computer Science 2018-07-11 Guoqing Zheng , Yiming Yang , Jaime Carbonell

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…

Machine Learning · Statistics 2022-04-28 Edmond Cunningham , Renos Zabounidis , Abhinav Agrawal , Madalina Fiterau , Daniel Sheldon

Deep Gaussian processes (DGPs), a hierarchical composition of GP models, have successfully boosted the expressive power of their single-layer counterpart. However, it is impossible to perform exact inference in DGPs, which has motivated the…

Machine Learning · Computer Science 2021-05-27 Haibin Yu , Dapeng Liu , Yizhou Chen , Bryan Kian Hsiang Low , Patrick Jaillet

In the past few years, deep generative models, such as generative adversarial networks \autocite{GAN}, variational autoencoders \autocite{vaepaper}, and their variants, have seen wide adoption for the task of modelling complex data…

Machine Learning · Statistics 2020-09-02 Guilherme G. P. Freitas Pires , Mário A. T. Figueiredo

This paper introduces a generative model equivariant to Euclidean symmetries: E(n) Equivariant Normalizing Flows (E-NFs). To construct E-NFs, we take the discriminative E(n) graph neural networks and integrate them as a differential…

Machine Learning · Computer Science 2022-01-17 Victor Garcia Satorras , Emiel Hoogeboom , Fabian B. Fuchs , Ingmar Posner , Max Welling
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