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Diffusion models are commonly interpreted as learning the score function, i.e., the gradient of the log-density of noisy data. However, this assumption implies that the target of learning is a conservative vector field, which is not…

Machine Learning · Computer Science 2025-09-03 An B. Vuong , Michael T. McCann , Javier E. Santos , Yen Ting Lin

Normalising flows (NFS) map two density functions via a differentiable bijection whose Jacobian determinant can be computed efficiently. Recently, as an alternative to hand-crafted bijections, Huang et al. (2018) proposed neural…

Machine Learning · Statistics 2019-04-10 Nicola De Cao , Ivan Titov , Wilker Aziz

Modeling transformations between arbitrary data distributions is a fundamental scientific challenge, arising in applications like drug discovery and evolutionary simulation. While flow matching offers a natural framework for this task, its…

Machine Learning · Computer Science 2025-10-09 Shiye Su , Yuhui Zhang , Linqi Zhou , Rajesh Ranganath , Serena Yeung-Levy

Generative models are a promising tool to address the sampling problem in multi-body and condensed-matter systems in the framework of statistical mechanics. In this work, we show that normalizing flows can be used to learn a transformation…

Computational Physics · Physics 2022-08-23 Alessandro Coretti , Sebastian Falkner , Phillip Geissler , Christoph Dellago

Normalizing Flows provide a principled framework for high-dimensional density estimation and generative modeling by constructing invertible transformations with tractable Jacobian determinants. We propose Fractal Flow, a novel normalizing…

Machine Learning · Statistics 2025-08-28 Binhui Zhang , Jianwei Ma

Normalizing flows have been successfully modeling a complex probability distribution as an invertible transformation of a simple base distribution. However, there are often applications that require more than invertibility. For instance,…

Machine Learning · Computer Science 2023-04-12 Seongmin Hong , Se Young Chun

We propose a simple algorithm to train stochastic neural networks to draw samples from given target distributions for probabilistic inference. Our method is based on iteratively adjusting the neural network parameters so that the output…

Machine Learning · Statistics 2017-11-01 Yihao Feng , Dilin Wang , Qiang Liu

In this paper we propose Discretely Indexed flows (DIF) as a new tool for solving variational estimation problems. Roughly speaking, DIF are built as an extension of Normalizing Flows (NF), in which the deterministic transport becomes…

Machine Learning · Statistics 2022-04-05 Elouan Argouarc'h , François Desbouvries , Eric Barat , Eiji Kawasaki , Thomas Dautremer

Efficient sampling of the Boltzmann distribution of molecular systems is a long-standing challenge. Recently, instead of generating long molecular dynamics simulations, generative machine learning methods such as normalizing flows have been…

Machine Learning · Computer Science 2024-08-06 Henrik Schopmans , Pascal Friederich

Mean field control (MFC) problems have vast applications in artificial intelligence, engineering, and economics, while solving MFC problems accurately and efficiently in high-dimensional spaces remains challenging. This work introduces…

Optimization and Control · Mathematics 2025-03-26 Jiaxi Zhao , Mo Zhou , Xinzhe Zuo , Wuchen Li

Normalizing flows provide an elegant approach to generative modeling that allows for efficient sampling and exact density evaluation of unknown data distributions. However, current techniques have significant limitations in their…

Machine Learning · Computer Science 2022-06-22 Sahil Sidheekh , Chris B. Dock , Tushar Jain , Radu Balan , Maneesh K. Singh

In order to sample from an unnormalized probability density function, we propose to combine continuous normalizing flows (CNFs) with rejection-resampling steps based on importance weights. We relate the iterative training of CNFs with…

Machine Learning · Statistics 2025-08-14 Johannes Hertrich , Robert Gruhlke

Although many deep-learning-based super-resolution approaches have been proposed in recent years, because no ground truth is available in the inference stage, few can quantify the errors and uncertainties of the super-resolved results. For…

Image and Video Processing · Electrical Eng. & Systems 2023-08-10 Jingyi Shen , Han-Wei Shen

We propose a continuous normalizing flow for sampling from the high-dimensional probability distributions of Quantum Field Theories in Physics. In contrast to the deep architectures used so far for this task, our proposal is based on a…

Machine Learning · Computer Science 2021-11-29 Pim de Haan , Corrado Rainone , Miranda C. N. Cheng , Roberto Bondesan

We introduce Random Projection Flows (RPFs), a principled framework for injective normalizing flows that leverages tools from random matrix theory and the geometry of random projections. RPFs employ random semi-orthogonal matrices, drawn…

Machine Learning · Computer Science 2025-11-26 Ahmad Ayaz Amin , Baha Uddin Kazi

Scene flow estimation is an essential ingredient for a variety of real-world applications, especially for autonomous agents, such as self-driving cars and robots. While recent scene flow estimation approaches achieve a reasonable accuracy,…

Computer Vision and Pattern Recognition · Computer Science 2024-10-07 Yushan Zhang , Bastian Wandt , Maria Magnusson , Michael Felsberg

This paper presents a parameter scan technique for BSM signal models based on normalizing flow. Normalizing flow is a type of deep learning model that transforms a simple probability distribution into a complex probability distribution as…

Data Analysis, Statistics and Probability · Physics 2024-09-23 Masahiko Saito , Masahiro Morinaga , Tomoe Kishimoto , Junichi Tanaka

The Boltzmann distribution of a protein provides a roadmap to all of its functional states. Normalizing flows are a promising tool for modeling this distribution, but current methods are intractable for typical pharmacological targets; they…

Machine Learning · Computer Science 2024-01-10 Joseph C. Kim , David Bloore , Karan Kapoor , Jun Feng , Ming-Hong Hao , Mengdi Wang

Sampling from unnormalised discrete distributions is a fundamental problem across various domains. While Markov chain Monte Carlo offers a principled approach, it often suffers from slow mixing and poor convergence. In this paper, we…

Machine Learning · Computer Science 2025-10-23 Zijing Ou , Ruixiang Zhang , Yingzhen Li

Analyzing and interpreting time-dependent stochastic data requires accurate and robust density estimation. In this paper we extend the concept of normalizing flows to so-called temporal Normalizing Flows (tNFs) to estimate time dependent…

Computational Physics · Physics 2019-12-20 Gert-Jan Both , Remy Kusters