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Due to the success of generative flows to model data distributions, they have been explored in inverse problems. Given a pre-trained generative flow, previous work proposed to minimize the 2-norm of the latent variables as a regularization…

Computer Vision and Pattern Recognition · Computer Science 2022-05-30 José A. Chávez

Recent advances in inverse problem solving have increasingly adopted flow priors over diffusion models due to their ability to construct straight probability paths from noise to data, thereby enhancing efficiency in both training and…

Computer Vision and Pattern Recognition · Computer Science 2025-11-11 Hossein Askari , Yadan Luo , Hongfu Sun , Fred Roosta

A normalizing flow models a complex probability density as an invertible transformation of a simple density. The invertibility means that we can evaluate densities and generate samples from a flow. In practice, autoregressive flow-based…

Machine Learning · Statistics 2019-06-06 Conor Durkan , Artur Bekasov , Iain Murray , George Papamakarios

Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled…

Machine Learning · Computer Science 2023-05-31 Matthias Kirchler , Christoph Lippert , Marius Kloft

Generative modeling techniques such as Diffusion and Flow Matching have achieved significant successes in generating designable and diverse protein backbones. However, many current models are computationally expensive, requiring hundreds or…

Biomolecules · Quantitative Biology 2025-10-30 Junhua Chen , Simon Mathis , Charles Harris , Kieran Didi , Pietro Lio

Continuous Normalizing Flows (CNFs) enable elegant generative modeling but remain bottlenecked by slow sampling: producing a single sample requires solving a nonlinear ODE with hundreds of function evaluations. Recent approaches such as…

Machine Learning · Computer Science 2025-10-23 Erkan Turan , Aristotelis Siozopoulos , Louis Martinez , Julien Gaubil , Emery Pierson , Maks Ovsjanikov

Generative Flow Networks (GFlowNets), a new family of probabilistic samplers, have demonstrated remarkable capabilities to generate diverse sets of high-reward candidates, in contrast to standard return maximization approaches (e.g.,…

Machine Learning · Computer Science 2025-02-25 Haoran He , Can Chang , Huazhe Xu , Ling Pan

Deep generative models complement Markov-chain-Monte-Carlo methods for efficiently sampling from high-dimensional distributions. Among these methods, explicit generators, such as Normalising Flows (NFs), in combination with the Metropolis…

Machine Learning · Computer Science 2024-05-29 Vikas Kanaujia , Mathias S. Scheurer , Vipul Arora

Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…

Machine Learning · Statistics 2025-06-10 Grigory Bartosh , Dmitry Vetrov , Christian A. Naesseth

Normalizing flows are a class of probabilistic generative models which allow for both fast density computation and efficient sampling and are effective at modelling complex distributions like images. A drawback among current methods is…

Computer Vision and Pattern Recognition · Computer Science 2020-10-28 Jason J. Yu , Konstantinos G. Derpanis , Marcus A. Brubaker

Continuous normalizing flows (CNFs) construct invertible mappings between an arbitrary complex distribution and an isotropic Gaussian distribution using Neural Ordinary Differential Equations (neural ODEs). It has not been tractable on…

Computer Vision and Pattern Recognition · Computer Science 2022-03-29 Shian Du , Yihong Luo , Wei Chen , Jian Xu , Delu Zeng

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…

Machine Learning · Statistics 2021-03-18 Cheng Lu , Jianfei Chen , Chongxuan Li , Qiuhao Wang , Jun Zhu

In this paper, we present a new class of invertible transformations with an application to flow-based generative models. We indicate that many well-known invertible transformations in reversible logic and reversible neural networks could be…

Machine Learning · Computer Science 2021-07-13 Jakub M. Tomczak

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…

Geophysics · Physics 2022-03-31 Ali Siahkoohi , Rafael Orozco , Gabrio Rizzuti , Felix J. Herrmann

We apply a unified machine-learning framework based on Normalizing Flows (NFs) for the event-by-event reconstruction of invisible momenta and the subsequent evaluation of spin-sensitive observables in top-quark pair and dark-matter (DM)…

High Energy Physics - Phenomenology · Physics 2025-10-14 E. Abasov , L. Dudko , E. Iudin , A. Markina , P. Volkov , G. Vorotnikov , M. Perfilov , A. Zaborenko

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…

Machine Learning · Statistics 2019-12-03 Conor Durkan , Artur Bekasov , Iain Murray , George Papamakarios

Likelihood-based deep generative models have been widely investigated for Image Anomaly Detection (IAD), particularly Normalizing Flows, yet their strict architectural invertibility needs often constrain scalability, particularly in…

Computer Vision and Pattern Recognition · Computer Science 2026-04-15 Liangwei Li , Lin Liu , Hanzhe Liang , Juanxiu Liu , Jing Zhang , Ruqian Hao , Xiaohui Du , Yong Liu , Pan Li

Flow-based generative models are an important class of exact inference models that admit efficient inference and sampling for image synthesis. Owing to the efficiency constraints on the design of the flow layers, e.g. split coupling flow…

Machine Learning · Computer Science 2020-04-09 Shweta Mahajan , Apratim Bhattacharyya , Mario Fritz , Bernt Schiele , Stefan Roth

Generative models can produce nonsensical text, unrealistic images, and unstable materials faster than simulation or human review can absorb; without per-sample confidence, trust erodes. Existing fixes run $k$ ensembles or stochastic…

Machine Learning · Statistics 2026-05-19 Friso de Kruiff , Dario Coscia , Max Welling , Erik Bekkers

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies…

Machine Learning · Statistics 2021-12-01 Jonas Köhler , Andreas Krämer , Frank Noé