{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T13:57:26Z","timestamp":1784901446784,"version":"3.55.0"},"reference-count":108,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"11","license":[{"start":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T00:00:00Z","timestamp":1635724800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T00:00:00Z","timestamp":1635724800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T00:00:00Z","timestamp":1635724800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Pattern Anal. Mach. Intell."],"published-print":{"date-parts":[[2021,11,1]]},"DOI":"10.1109\/tpami.2020.2992934","type":"journal-article","created":{"date-parts":[[2020,5,7]],"date-time":"2020-05-07T20:18:01Z","timestamp":1588882681000},"page":"3964-3979","source":"Crossref","is-referenced-by-count":911,"title":["Normalizing Flows: An Introduction and Review of Current Methods"],"prefix":"10.1109","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1934-4842","authenticated-orcid":false,"given":"Ivan","family":"Kobyzev","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Simon J.D.","family":"Prince","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marcus A.","family":"Brubaker","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2015.123"},{"key":"ref38","article-title":"Variational inference with orthogonal normalizing flows","author":"hasenclever","year":"2017","journal-title":"Workshop on Bayesian Deep Learning"},{"key":"ref33","first-page":"2672","article-title":"Generative adversarial nets","author":"goodfellow","year":"2014","journal-title":"Proc 27th Int Conf Neural Inf Process Syst"},{"key":"ref32","first-page":"2211","article-title":"The reversible residual network: Backpropagation without storing activations","author":"gomez","year":"2017","journal-title":"Proc 31st Int Conf Neural Inf Process Syst"},{"key":"ref31","first-page":"881","article-title":"MADE: Masked autoencoder for distribution estimation","author":"germain","year":"2015","journal-title":"Proc 32nd Int Conf Mach Learn"},{"key":"ref30","article-title":"Normalizing flows on riemannian manifolds","author":"gemici","year":"2016"},{"key":"ref37","article-title":"Learning across scales - A multiscale method for convolution neural networks","author":"haber","year":"2018","journal-title":"Proc AAAI Conf Artif Intell"},{"key":"ref36","article-title":"Flow-GAN: Combining maximum likelihood and adversarial learning in generative models","author":"grover","year":"2018","journal-title":"Proc AAAI Conf Artif Intell"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/2.2.123"},{"key":"ref34","article-title":"FFJORD: Free-form continuous dynamics for scalable reversible generative models","author":"grathwohl","year":"2019","journal-title":"Proc Int Conf Learn Representations"},{"key":"ref28","article-title":"Reparameterizing distributions on lie groups","author":"falorsi","year":"2019"},{"key":"ref27","article-title":"Universal audio synthesizer control with normalizing flows","author":"esling","year":"2019"},{"key":"ref29","article-title":"How to train your neural ODE","author":"finlay","year":"2020"},{"key":"ref20","article-title":"Density estimation using real NVP","author":"dinh","year":"2017","journal-title":"Proc Int Conf Learn Representations"},{"key":"ref22","article-title":"UCI machine learning repository","author":"dua","year":"2017"},{"key":"ref21","article-title":"A RAD approach to deep mixture models","author":"dinh","year":"2019","journal-title":"Proc Int Conf Learn Representations Workshop"},{"key":"ref24","article-title":"Cubic-spline flows","author":"durkan","year":"2019","journal-title":"Workshop Invertible Neural Networks Normalizing Flows (ICML)"},{"key":"ref23","first-page":"3140","article-title":"Augmented neural ODEs","author":"dupont","year":"2019","journal-title":"Proc Int Conf Neural Inf Process"},{"key":"ref101","article-title":"Riemannian normalizing flow on variational wasserstein autoencoder for text modeling","author":"wang","year":"2019"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1007\/s40304-017-0103-z"},{"key":"ref100","doi-asserted-by":"publisher","DOI":"10.1109\/JAS.2017.7510583"},{"key":"ref25","first-page":"7511","article-title":"Neural spline flows","author":"durkan","year":"2019","journal-title":"Proc Int Conf Neural Inf Process"},{"key":"ref50","first-page":"2235","article-title":"Pathwise derivatives beyond the reparameterization trick","author":"jankowiak","year":"2018","journal-title":"Proc 35th Int Conf Mach Learn"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.125.121601"},{"key":"ref59","author":"koller","year":"2009","journal-title":"Probabilistic Graphical Models"},{"key":"ref58","article-title":"Equivariant flows: Sampling configurations for multi-body systems with symmetric energies","author":"k\u00f6hler","year":"2019","journal-title":"Workshop Mach Learn Physical Sciences (NeurIPS)"},{"key":"ref57","first-page":"10 215","article-title":"Glow: Generative flow with invertible 1x1 convolutions","author":"kingma","year":"2018","journal-title":"Proc Int Conf Neural Inf Process"},{"key":"ref56","first-page":"4743","article-title":"Improved variational inference with inverse autoregressive flow","author":"kingma","year":"2016","journal-title":"Proc Int Conf Neural Inf Process"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1561\/9781680836233"},{"key":"ref54","article-title":"Auto-encoding variational bayes","author":"kingma","year":"2014","journal-title":"Proc 2nd Int Conf Learn Representations"},{"key":"ref53","first-page":"3370","article-title":"FloWaveNet: A generative flow for raw audio","author":"kim","year":"2018","journal-title":"Proc 36th Int Conf Mach Learn"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809187"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref4","first-page":"214","article-title":"Wasserstein Generative Adversarial Networks","author":"arjovsky","year":"2017","journal-title":"Proc 34th Int Conf Mach Learn"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/PL00013195"},{"key":"ref6","article-title":"Semi-conditional normalizing flows for semi-supervised learning","author":"atanov","year":"2019","journal-title":"Workshop Invertible Neural Nets Normalizing Flows (ICML)"},{"key":"ref5","author":"arnold","year":"1978","journal-title":"Ordinary Differential Equations"},{"key":"ref8","article-title":"Estimating or propagating gradients through stochastic neurons for conditional computation","author":"bengio","year":"2013"},{"key":"ref49","first-page":"3009","article-title":"Sum-of-squares polynomial flow","author":"jaini","year":"2019","journal-title":"Proc 36th Int Conf Mach Learn"},{"key":"ref7","article-title":"Invertible residual networks","author":"behrmann","year":"2019","journal-title":"Proc 36th Int Conf Mach Learn"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1070\/SM2005v196n03ABEH000882"},{"key":"ref46","first-page":"448","article-title":"Batch normalization: Accelerating deep network training by reducing internal covariate shift","author":"ioffe","year":"2015","journal-title":"Proc 32nd Int Conf Mach Learn"},{"key":"ref45","first-page":"2078","article-title":"Neural autoregressive flows","author":"huang","year":"2018","journal-title":"Proc 35th Int Conf Mach Learn"},{"key":"ref48","article-title":"Tails of triangular flows","author":"jaini","year":"2019"},{"key":"ref47","article-title":"i-RevNet: Deep invertible networks","author":"jacobsen","year":"2018","journal-title":"Proc Int Conf Learn Representations"},{"key":"ref42","first-page":"2771","article-title":"Emerging convolutions for generative normalizing flows","author":"hoogeboom","year":"2019","journal-title":"Proc 36th Int Conf Mach Learn"},{"key":"ref41","first-page":"2722","article-title":"Flow++: Improving flow-based generative models with variational dequantization and architecture design","author":"ho","year":"2019","journal-title":"Proc 36th Int Conf Mach Learn"},{"key":"ref44","article-title":"Learning discrete distributions by dequantization","author":"hoogeboom","year":"2020"},{"key":"ref43","article-title":"Integer discrete flows and lossless compression","author":"hoogeboom","year":"2019","journal-title":"Proc 33rd Int Conf Neural Inf Process Syst"},{"key":"ref73","article-title":"Poincaré wasserstein autoencoder","author":"ovinnikov","year":"2018","journal-title":"NeurIPS Workshop on Bayesian Deep Learning (NeurIPS BDL)"},{"key":"ref72","author":"oksendal","year":"1992","journal-title":"Stochastic Differential Equations (3rd Ed ) An Introduction with Applications"},{"key":"ref71","doi-asserted-by":"crossref","DOI":"10.1126\/science.aaw1147","article-title":"Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning","volume":"365","author":"no\u00e9","year":"2019","journal-title":"Science"},{"key":"ref70","article-title":"Improving exploration in soft-actor-critic with normalizing flows policies","author":"nadeem ward","year":"2019","journal-title":"Workshop Invertible Neural Nets Normalizing Flows (ICML)"},{"key":"ref76","article-title":"Neural stochastic differential equations","author":"peluchetti","year":"2019"},{"key":"ref77","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP.2019.8683143"},{"key":"ref74","first-page":"2335","article-title":"Masked autoregressive flow for density estimation","author":"papamakarios","year":"2017","journal-title":"Proc 31st Int Conf Neural Inf Process Syst"},{"key":"ref75","article-title":"Normalizing flows for probabilistic modeling and inference","author":"papamakarios","year":"2019"},{"key":"ref78","first-page":"1530","article-title":"Variational inference with normalizing flows","author":"rezende","year":"2015","journal-title":"Proc 32nd Int Conf Mach Learn"},{"key":"ref79","article-title":"Normalizing flows on tori and spheres","author":"rezende","year":"2020"},{"key":"ref60","article-title":"VideoFlow: A flow-based generative model for video","author":"kumar","year":"2019","journal-title":"Workshop Invertible Neural Nets Normalizing Flows (ICML)"},{"key":"ref62","article-title":"Scalable gradients for stochastic differential equations","author":"li","year":"2020"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-7248-3_10"},{"key":"ref63","first-page":"4104","article-title":"Sliced-wasserstein flows: Nonparametric generative modeling via optimal transport and diffusions","author":"liutkus","year":"2019","journal-title":"Proc 36th Int Conf Mach Learn"},{"key":"ref64","article-title":"Rectifier nonlinearities improve neural network acoustic models","author":"maas","year":"2013","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref65","article-title":"GraphNVP: An invertible flow model for generating molecular graphs","author":"madhawa","year":"2019"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2001.937655"},{"key":"ref67","article-title":"Leveraging exploration in off-policy algorithms via normalizing flows","author":"mazoure","year":"2019","journal-title":"Proc 3rd Conf Robot Learn"},{"key":"ref68","first-page":"95","article-title":"Certain properties of triangular transformations of measures","volume":"14","author":"medvedev","year":"2008","journal-title":"The theory of stochastic process I"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/100783522"},{"key":"ref69","article-title":"Neural importance sampling","volume":"38","author":"m\u00fcller","year":"2018","journal-title":"ACM Trans Graph"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2019.00326"},{"key":"ref95","article-title":"Conditional density estimation with Bayesian normalising flows","author":"trippe","year":"2017","journal-title":"Workshop on Bayesian Deep Learning"},{"key":"ref108","first-page":"7673","article-title":"Latent normalizing flows for discrete sequences","author":"ziegler","year":"2019","journal-title":"Proc 36th Int Conf Mach Learn"},{"key":"ref94","article-title":"Discrete flows: Invertible generative models of discrete data","author":"tran","year":"2019","journal-title":"Proc Int Conf Learn Representations Workshop"},{"key":"ref107","article-title":"Convolutional normalizing flows","author":"zheng","year":"2018","journal-title":"Workshop Theoretical Foundations Applications Deep Generative Models (ICML)"},{"key":"ref93","article-title":"Randomized value functions via multiplicative normalizing flows","author":"touati","year":"2019","journal-title":"Proc Conf Uncertainty Artif Intell"},{"key":"ref106","article-title":"Approximation capabilities of neural ordinary differential equations","author":"zhang","year":"2019"},{"key":"ref92","article-title":"Improving variational auto-encoders using householder flow","author":"tomczak","year":"2016"},{"key":"ref105","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.101.123005"},{"key":"ref91","article-title":"Improving variational auto-encoders using convex combination linear inverse autoregressive flow","author":"tomczak","year":"2017","journal-title":"Benelearn"},{"key":"ref104","doi-asserted-by":"publisher","DOI":"10.1063\/5.0018903"},{"key":"ref90","article-title":"Wasserstein auto-encoders","author":"tolstikhin","year":"2018","journal-title":"Proc Int Conf Learn Representations"},{"key":"ref103","first-page":"681","article-title":"Bayesian learning via stochastic gradient langevin dynamics","author":"welling","year":"2011","journal-title":"Proc 28th Int Conf Mach Learn"},{"key":"ref102","article-title":"Unconstrained monotonic neural networks","author":"wehenkel","year":"2019"},{"key":"ref98","first-page":"3918","article-title":"Parallel wavenet: Fast high-fidelity speech synthesis","author":"van den oord","year":"2017","journal-title":"Proc 35th Int Conf Mach Learn"},{"key":"ref99","author":"villani","year":"2003","journal-title":"Topics in Optimal Transportation (Graduate Studies in Mathematics 58)"},{"key":"ref96","article-title":"Neural stochastic differential equations: Deep latent gaussian models in the diffusion limit","author":"tzen","year":"2019"},{"key":"ref97","article-title":"Sylvester normalizing flows for variational inference","author":"van den berg","year":"2018","journal-title":"Proc Conf Uncertainty of Artificial Intelligence"},{"key":"ref10","article-title":"Latent variable modelling with hyperbolic normalizing flows","author":"bose","year":"2020"},{"key":"ref11","first-page":"10","article-title":"Generating sentences from a continuous space","author":"bowman","year":"2015","journal-title":"Proc 20th SIGNLL Conf Comput Natural Lang Learn"},{"key":"ref12","first-page":"2811","article-title":"Reversible architectures for arbitrarily deep residual neural networks","author":"chang","year":"2018","journal-title":"Proc AAAI Conf Artif Intell"},{"key":"ref13","article-title":"AntisymmetricRNN: A dynamical system view on recurrent neural networks","author":"chang","year":"2019","journal-title":"Proc Int Conf Learn Representations"},{"key":"ref14","article-title":"Continuous-time flows for efficient inference and density estimation","author":"chen","year":"2018","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref15","first-page":"6572","article-title":"Neural ordinary differential equations","author":"chen","year":"2018","journal-title":"Proc 32nd Int Conf Neural Inf Process Syst"},{"key":"ref16","article-title":"Residual flows for invertible generative modeling","author":"chen","year":"2019","journal-title":"Proc 33rd Int Conf Neural Inf Process Syst"},{"key":"ref82","first-page":"2234","article-title":"Improved techniques for training GANs","author":"salimans","year":"2016","journal-title":"Proc 30th Int Conf Neural Inf Process Syst"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2017.2765202"},{"key":"ref81","first-page":"1218","article-title":"Markov chain Monte Carlo and variational inference: Bridging the gap","author":"salimans","year":"2015","journal-title":"Proc 32nd Int Conf Mach Learn"},{"key":"ref18","article-title":"Dimensionality reduction flows","author":"das","year":"2019"},{"key":"ref84","first-page":"2256","article-title":"Deep unsupervised learning using nonequilibrium thermodynamics","author":"sohl-dickstein","year":"2015","journal-title":"Proc 32nd Int Conf Mach Learn"},{"key":"ref19","article-title":"NICE: Non-linear independent components estimation","author":"dinh","year":"2015","journal-title":"Proc Int Conf Learn Representations Workshop"},{"key":"ref83","article-title":"Deep diffeomorphic normalizing flows","author":"salman","year":"2018"},{"key":"ref80","article-title":"High-dimensional probability estimation with deep density models","author":"rippel","year":"2013"},{"key":"ref89","doi-asserted-by":"publisher","DOI":"10.4310\/CMS.2010.v8.n1.a11"},{"key":"ref85","first-page":"2639","article-title":"Inference via low-dimensional couplings","volume":"19","author":"spantini","year":"2017","journal-title":"J Mach Learn Res"},{"key":"ref86","author":"spivak","year":"1965","journal-title":"Calculus on Manifolds A Modern Approach to Classical Theorems of Advanced Calculus"},{"key":"ref87","doi-asserted-by":"publisher","DOI":"10.1023\/A:1009632428145"},{"key":"ref88","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.21423"}],"container-title":["IEEE Transactions on Pattern Analysis and Machine Intelligence"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/34\/9556112\/09089305.pdf?arnumber=9089305","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,10]],"date-time":"2022-05-10T14:49:25Z","timestamp":1652194165000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9089305\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,1]]},"references-count":108,"journal-issue":{"issue":"11"},"URL":"https:\/\/doi.org\/10.1109\/tpami.2020.2992934","relation":{},"ISSN":["0162-8828","2160-9292","1939-3539"],"issn-type":[{"value":"0162-8828","type":"print"},{"value":"2160-9292","type":"electronic"},{"value":"1939-3539","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,1]]}}}