Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models

Deep generative models are a class of techniques that train deep neural networks to model the distribution of training samples. Research has fragmented into various interconnected approaches, each of which make trade-offs including run-time, diversity, and architectural restrictions. In particular, this compendium covers energy-based models, variational autoencoders, generative adversarial networks, autoregressive models, normalizing flows, in addition to numerous hybrid approaches. These techniques are compared and contrasted, explaining the premises behind each and how they are interrelated, while reviewing current state-of-the-art advances and implementations.

[1]  Nicola De Cao,et al.  Block Neural Autoregressive Flow , 2019, UAI.

[2]  Gordon Wetzstein,et al.  Implicit Neural Representations with Periodic Activation Functions , 2020, NeurIPS.

[3]  Iain Murray,et al.  Cubic-Spline Flows , 2019, ICML 2019.

[4]  Mark Chen,et al.  Language Models are Few-Shot Learners , 2020, NeurIPS.

[5]  Sergey Ioffe,et al.  Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift , 2015, ICML.

[6]  Graham Neubig,et al.  Lagging Inference Networks and Posterior Collapse in Variational Autoencoders , 2019, ICLR.

[7]  Rémi Munos,et al.  Autoregressive Quantile Networks for Generative Modeling , 2018, ICML.

[8]  Oriol Vinyals,et al.  Neural Discrete Representation Learning , 2017, NIPS.

[9]  Shiyu Chang,et al.  TransGAN: Two Transformers Can Make One Strong GAN , 2021, ArXiv.

[10]  Yoshua Bengio,et al.  Small-GAN: Speeding Up GAN Training Using Core-sets , 2019, ICML.

[11]  Yang Lu,et al.  Cooperative Training of Descriptor and Generator Networks , 2016, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Ilya Sutskever,et al.  Generating Long Sequences with Sparse Transformers , 2019, ArXiv.

[13]  Lukasz Kaiser,et al.  Attention is All you Need , 2017, NIPS.

[14]  Heiga Zen,et al.  Parallel WaveNet: Fast High-Fidelity Speech Synthesis , 2017, ICML.

[15]  Razvan Pascanu,et al.  A RAD approach to deep mixture models , 2019, DGS@ICLR.

[16]  David Duvenaud,et al.  FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models , 2018, ICLR.

[17]  Yee Whye Teh,et al.  Bayesian Learning via Stochastic Gradient Langevin Dynamics , 2011, ICML.

[18]  Aapo Hyvärinen,et al.  Estimation of Non-Normalized Statistical Models by Score Matching , 2005, J. Mach. Learn. Res..

[19]  Yang Song,et al.  Sliced Score Matching: A Scalable Approach to Density and Score Estimation , 2019, UAI.

[20]  Richard E. Turner,et al.  Two problems with variational expectation maximisation for time-series models , 2011 .

[21]  Eric Nalisnick,et al.  Normalizing Flows for Probabilistic Modeling and Inference , 2019, J. Mach. Learn. Res..

[22]  Maxim Raginsky,et al.  Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit , 2019, ArXiv.

[23]  Jan Kautz,et al.  NVAE: A Deep Hierarchical Variational Autoencoder , 2020, NeurIPS.

[24]  Dustin Tran,et al.  Variational Gaussian Process , 2015, ICLR.

[25]  Prafulla Dhariwal,et al.  Improved Denoising Diffusion Probabilistic Models , 2021, ICML.

[26]  Stefano Ermon,et al.  InfoVAE: Balancing Learning and Inference in Variational Autoencoders , 2019, AAAI.

[27]  Alexander M. Rush,et al.  Latent Normalizing Flows for Discrete Sequences , 2019, ICML.

[28]  John P. Cunningham,et al.  The continuous Bernoulli: fixing a pervasive error in variational autoencoders , 2019, NeurIPS.

[29]  Yoshua Bengio,et al.  Generative Adversarial Nets , 2014, NIPS.

[30]  Cho-Jui Hsieh,et al.  Improving the Speed and Quality of GAN by Adversarial Training , 2020, ArXiv.

[31]  David Vázquez,et al.  PixelVAE: A Latent Variable Model for Natural Images , 2016, ICLR.

[32]  Stefano Ermon,et al.  Learning Hierarchical Features from Deep Generative Models , 2017, ICML.

[33]  Nal Kalchbrenner,et al.  Generating High Fidelity Images with Subscale Pixel Networks and Multidimensional Upscaling , 2018, ICLR.

[34]  C. Villani Optimal Transport: Old and New , 2008 .

[35]  Yee Whye Teh,et al.  Generative Models as Distributions of Functions , 2021, ArXiv.

[36]  Xingjian Li,et al.  OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transport , 2020, ArXiv.

[37]  Michael I. Jordan,et al.  An Introduction to Variational Methods for Graphical Models , 1999, Machine Learning.

[38]  Lukasz Kaiser,et al.  Rethinking Attention with Performers , 2020, ArXiv.

[39]  Tian Han,et al.  Learning Latent Space Energy-Based Prior Model , 2020, NeurIPS.

[40]  Jakub M. Tomczak,et al.  Variational Inference with Orthogonal Normalizing Flows , 2017 .

[41]  Max Welling,et al.  VAE with a VampPrior , 2017, AISTATS.

[42]  Sepp Hochreiter,et al.  GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium , 2017, NIPS.

[43]  Sergio Gomez Colmenarejo,et al.  Parallel Multiscale Autoregressive Density Estimation , 2017, ICML.

[44]  Truyen Tran,et al.  Catastrophic forgetting and mode collapse in GANs , 2020, 2020 International Joint Conference on Neural Networks (IJCNN).

[45]  Jason Yosinski,et al.  Metropolis-Hastings Generative Adversarial Networks , 2018, ICML.

[46]  Stefano Ermon,et al.  Improved Autoregressive Modeling with Distribution Smoothing , 2021, ICLR.

[47]  Erik Nijkamp,et al.  Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Model , 2019, NeurIPS.

[48]  Erik Nijkamp,et al.  Learning Energy-based Model with Flow-based Backbone by Neural Transport MCMC , 2020, ArXiv.

[49]  Arthur Gretton,et al.  Demystifying MMD GANs , 2018, ICLR.

[50]  David P. Wipf,et al.  Diagnosing and Enhancing VAE Models , 2019, ICLR.

[51]  Thomas Brox,et al.  Generating Images with Perceptual Similarity Metrics based on Deep Networks , 2016, NIPS.

[52]  Alexander M. Rush,et al.  Semi-Amortized Variational Autoencoders , 2018, ICML.

[53]  Pascal Vincent,et al.  Generalized Denoising Auto-Encoders as Generative Models , 2013, NIPS.

[54]  Alex Krizhevsky,et al.  Learning Multiple Layers of Features from Tiny Images , 2009 .

[55]  Cho-Jui Hsieh,et al.  Rob-GAN: Generator, Discriminator, and Adversarial Attacker , 2018, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[56]  Simon Osindero,et al.  Conditional Generative Adversarial Nets , 2014, ArXiv.

[57]  Nando de Freitas,et al.  On Autoencoders and Score Matching for Energy Based Models , 2011, ICML.

[58]  Ryan Prenger,et al.  Waveglow: A Flow-based Generative Network for Speech Synthesis , 2018, ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[59]  Lantao Yu,et al.  Training Deep Energy-Based Models with f-Divergence Minimization , 2020, ICML.

[60]  Mohammad Norouzi,et al.  Dream to Control: Learning Behaviors by Latent Imagination , 2019, ICLR.

[61]  Yoshua Bengio,et al.  Your GAN is Secretly an Energy-based Model and You Should use Discriminator Driven Latent Sampling , 2020, NeurIPS.

[62]  Charlie Nash,et al.  Autoregressive Energy Machines , 2019, ICML.

[63]  Tero Karras,et al.  Training Generative Adversarial Networks with Limited Data , 2020, NeurIPS.

[64]  Léon Bottou,et al.  Towards Principled Methods for Training Generative Adversarial Networks , 2017, ICLR.

[65]  Fu Jie Huang,et al.  A Tutorial on Energy-Based Learning , 2006 .

[66]  Koray Kavukcuoglu,et al.  Pixel Recurrent Neural Networks , 2016, ICML.

[67]  Iain Murray,et al.  Neural Spline Flows , 2019, NeurIPS.

[68]  Yann LeCun,et al.  Energy-based Generative Adversarial Network , 2016, ICLR.

[69]  Ilya Sutskever,et al.  On the Convergence Properties of Contrastive Divergence , 2010, AISTATS.

[70]  David Duvenaud,et al.  Residual Flows for Invertible Generative Modeling , 2019, NeurIPS.

[71]  Yang Song,et al.  MintNet: Building Invertible Neural Networks with Masked Convolutions , 2019, NeurIPS.

[72]  Aapo Hyvärinen,et al.  Noise-contrastive estimation: A new estimation principle for unnormalized statistical models , 2010, AISTATS.

[73]  R. Tweedie,et al.  Exponential convergence of Langevin distributions and their discrete approximations , 1996 .

[74]  Wojciech Zaremba,et al.  Improved Techniques for Training GANs , 2016, NIPS.

[75]  Adam M. Oberman,et al.  How to Train Your Neural ODE: the World of Jacobian and Kinetic Regularization , 2020, ICML.

[76]  Max Welling,et al.  Markov Chain Monte Carlo and Variational Inference: Bridging the Gap , 2014, ICML.

[77]  Thomas Müller,et al.  Neural Importance Sampling , 2018, ACM Trans. Graph..

[78]  Ole Winther,et al.  BIVA: A Very Deep Hierarchy of Latent Variables for Generative Modeling , 2019, NeurIPS.

[79]  Zhenan Sun,et al.  A Review on Generative Adversarial Networks: Algorithms, Theory, and Applications , 2020, IEEE Transactions on Knowledge and Data Engineering.

[80]  Timo Aila,et al.  A Style-Based Generator Architecture for Generative Adversarial Networks , 2018, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[81]  Ruslan Salakhutdinov,et al.  Importance Weighted Autoencoders , 2015, ICLR.

[82]  Ole Winther,et al.  Ladder Variational Autoencoders , 2016, NIPS.

[83]  Stefano Ermon,et al.  A-NICE-MC: Adversarial Training for MCMC , 2017, NIPS.

[84]  Tian Han,et al.  Alternating Back-Propagation for Generator Network , 2016, AAAI.

[85]  Surya Ganguli,et al.  Deep Unsupervised Learning using Nonequilibrium Thermodynamics , 2015, ICML.

[86]  Zengyi Li,et al.  Learning Energy-Based Models in High-Dimensional Spaces with Multi-scale Denoising Score Matching , 2019, 1910.07762.

[87]  Guodong Zhang,et al.  On Solving Minimax Optimization Locally: A Follow-the-Ridge Approach , 2019, ICLR.

[88]  Max Welling,et al.  Sylvester Normalizing Flows for Variational Inference , 2018, UAI.

[89]  Ying Nian Wu,et al.  Learning Energy-Based Models by Diffusion Recovery Likelihood , 2020, ICLR.

[90]  Alexia Jolicoeur-Martineau,et al.  The relativistic discriminator: a key element missing from standard GAN , 2018, ICLR.

[91]  Jascha Sohl-Dickstein,et al.  Invertible Convolutional Flow , 2019, NeurIPS.

[92]  Aaron C. Courville,et al.  Augmented Normalizing Flows: Bridging the Gap Between Generative Flows and Latent Variable Models , 2020, ArXiv.

[93]  Paul Babyn,et al.  Generative Adversarial Network in Medical Imaging: A Review , 2018, Medical Image Anal..

[94]  Raymond Y. K. Lau,et al.  Least Squares Generative Adversarial Networks , 2016, 2017 IEEE International Conference on Computer Vision (ICCV).

[95]  Guoping Qiu,et al.  Spectral regularization for combating mode collapse in GANs , 2020, Image Vis. Comput..

[96]  Jonathan T. Barron,et al.  Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains , 2020, NeurIPS.

[97]  Yee Whye Teh,et al.  A Fast Learning Algorithm for Deep Belief Nets , 2006, Neural Computation.

[98]  Yang Lu,et al.  A Theory of Generative ConvNet , 2016, ICML.

[99]  Diederik P. Kingma,et al.  How to Train Your Energy-Based Models , 2021, ArXiv.

[100]  L. Duan Transport Monte Carlo , 2019, 1907.10448.

[101]  Sergey Levine,et al.  Stochastic Adversarial Video Prediction , 2018, ArXiv.

[102]  Shakir Mohamed,et al.  Variational Inference with Normalizing Flows , 2015, ICML.

[103]  Samy Bengio,et al.  Density estimation using Real NVP , 2016, ICLR.

[104]  Han Fang,et al.  Linformer: Self-Attention with Linear Complexity , 2020, ArXiv.

[105]  C. Villani Topics in Optimal Transportation , 2003 .

[106]  Alex Graves,et al.  DRAW: A Recurrent Neural Network For Image Generation , 2015, ICML.

[107]  Frederick R. Forst,et al.  On robust estimation of the location parameter , 1980 .

[108]  Yuichi Yoshida,et al.  Spectral Normalization for Generative Adversarial Networks , 2018, ICLR.

[109]  Yaoliang Yu,et al.  Sum-of-Squares Polynomial Flow , 2019, ICML.

[110]  Oliver Wang,et al.  MSG-GAN: Multi-Scale Gradients for Generative Adversarial Networks , 2019, 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[111]  VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Models , 2020, ArXiv.

[112]  Jeff Donahue,et al.  Large Scale GAN Training for High Fidelity Natural Image Synthesis , 2018, ICLR.

[113]  Sameer Singh,et al.  Image Augmentations for GAN Training , 2020, ArXiv.

[114]  Joshua V. Dillon,et al.  NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport , 2019, 1903.03704.

[115]  Michael Burke,et al.  DepthwiseGANs: Fast Training Generative Adversarial Networks for Realistic Image Synthesis , 2019, 2019 Southern African Universities Power Engineering Conference/Robotics and Mechatronics/Pattern Recognition Association of South Africa (SAUPEC/RobMech/PRASA).

[116]  Pieter Abbeel,et al.  Variational Lossy Autoencoder , 2016, ICLR.

[117]  Yang Song,et al.  Generative Modeling by Estimating Gradients of the Data Distribution , 2019, NeurIPS.

[118]  Ole Winther,et al.  SurVAE Flows: Surjections to Bridge the Gap between VAEs and Flows , 2020, NeurIPS.

[119]  M. L. Chambers The Mathematical Theory of Optimal Processes , 1965 .

[120]  David Duvenaud,et al.  Neural Ordinary Differential Equations , 2018, NeurIPS.

[121]  Bernhard Schölkopf,et al.  Deep Energy Estimator Networks , 2018, ArXiv.

[122]  Aleksander Madry,et al.  Towards Deep Learning Models Resistant to Adversarial Attacks , 2017, ICLR.

[123]  Rewon Child Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images , 2021, ICLR.

[124]  David Duvenaud,et al.  Invertible Residual Networks , 2018, ICML.

[125]  Xi Chen,et al.  PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications , 2017, ICLR.

[126]  Geoffrey E. Hinton,et al.  A New Learning Algorithm for Mean Field Boltzmann Machines , 2002, ICANN.

[127]  Song Han,et al.  Differentiable Augmentation for Data-Efficient GAN Training , 2020, NeurIPS.

[128]  Abhishek Kumar,et al.  Score-Based Generative Modeling through Stochastic Differential Equations , 2020, ICLR.

[129]  Yoshua Bengio,et al.  MelGAN: Generative Adversarial Networks for Conditional Waveform Synthesis , 2019, NeurIPS.

[130]  Mohammad Norouzi,et al.  No MCMC for me: Amortized sampling for fast and stable training of energy-based models , 2021, ICLR.

[131]  Ngai-Man Cheung,et al.  On Data Augmentation for GAN Training , 2020, IEEE Transactions on Image Processing.

[132]  Han Zhang,et al.  Self-Attention Generative Adversarial Networks , 2018, ICML.

[133]  George Em Karniadakis,et al.  Potential Flow Generator With L2 Optimal Transport Regularity for Generative Models , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[134]  Bernhard Schölkopf,et al.  From Variational to Deterministic Autoencoders , 2019, ICLR.

[135]  Petros Dellaportas,et al.  Gradient-based Adaptive Markov Chain Monte Carlo , 2019, NeurIPS.

[136]  Andriy Mnih,et al.  The Lipschitz Constant of Self-Attention , 2020, ICML.

[137]  Max Welling,et al.  Emerging Convolutions for Generative Normalizing Flows , 2019, ICML.

[138]  Rob Fergus,et al.  Deep Generative Image Models using a Laplacian Pyramid of Adversarial Networks , 2015, NIPS.

[139]  Dmitry Vetrov,et al.  The Implicit Metropolis-Hastings Algorithm , 2019, NeurIPS.

[140]  Jürgen Schmidhuber,et al.  Long Short-Term Memory , 1997, Neural Computation.

[141]  Yee Whye Teh,et al.  Augmented Neural ODEs , 2019, NeurIPS.

[142]  Jiaming Song,et al.  Denoising Diffusion Implicit Models , 2021, ICLR.

[143]  Richard Zemel,et al.  Learning the Stein Discrepancy for Training and Evaluating Energy-Based Models without Sampling , 2020, ICML.

[144]  Pieter Abbeel,et al.  Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design , 2019, ICML.

[145]  Tian Han,et al.  On the Anatomy of MCMC-based Maximum Likelihood Learning of Energy-Based Models , 2019, AAAI.

[146]  Lucas Theis,et al.  Amortised MAP Inference for Image Super-resolution , 2016, ICLR.

[147]  Kumar Krishna Agrawal,et al.  Discrete Flows: Invertible Generative Models of Discrete Data , 2019, DGS@ICLR.

[148]  Jakub M. Tomczak,et al.  The Convolution Exponential and Generalized Sylvester Flows , 2020, NeurIPS.

[149]  Jian Sun,et al.  Deep Residual Learning for Image Recognition , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[150]  P. J. Huber Robust Estimation of a Location Parameter , 1964 .

[151]  Igor Mordatch,et al.  Implicit Generation and Generalization with Energy Based Models , 2018 .

[152]  Xiaohua Zhai,et al.  Self-Supervised GANs via Auxiliary Rotation Loss , 2018, 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[153]  Sergey Levine,et al.  Stochastic Variational Video Prediction , 2017, ICLR.

[154]  Mark Chen,et al.  Distribution Augmentation for Generative Modeling , 2020, ICML.

[155]  Ryan P. Adams,et al.  SUMO: Unbiased Estimation of Log Marginal Probability for Latent Variable Models , 2020, ICLR.

[156]  Geoffrey E. Hinton Training Products of Experts by Minimizing Contrastive Divergence , 2002, Neural Computation.

[157]  Alexandre Lacoste,et al.  Neural Autoregressive Flows , 2018, ICML.

[158]  Nikolaos Pappas,et al.  Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention , 2020, ICML.

[159]  David Lopez-Paz,et al.  Optimizing the Latent Space of Generative Networks , 2017, ICML.

[160]  Yoshua Bengio,et al.  NICE: Non-linear Independent Components Estimation , 2014, ICLR.

[161]  Jaakko Lehtinen,et al.  Progressive Growing of GANs for Improved Quality, Stability, and Variation , 2017, ICLR.

[162]  Soumith Chintala,et al.  Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks , 2015, ICLR.

[163]  Jun Zhu,et al.  A Spectral Approach to Gradient Estimation for Implicit Distributions , 2018, ICML.

[164]  Yoshua Bengio,et al.  Deep Directed Generative Models with Energy-Based Probability Estimation , 2016, ArXiv.

[165]  Yoshua Bengio,et al.  SampleRNN: An Unconditional End-to-End Neural Audio Generation Model , 2016, ICLR.

[166]  Aaron C. Courville,et al.  Improved Training of Wasserstein GANs , 2017, NIPS.

[167]  Jun Zhu,et al.  VFlow: More Expressive Generative Flows with Variational Data Augmentation , 2020, ICML.

[168]  Colin Raffel,et al.  Towards GAN Benchmarks Which Require Generalization , 2020, ICLR.

[169]  Jaakko Lehtinen,et al.  Analyzing and Improving the Image Quality of StyleGAN , 2020, 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[170]  Mohammad Havaei,et al.  Learnable Explicit Density for Continuous Latent Space and Variational Inference , 2017, ArXiv.

[171]  Iain Murray,et al.  On Contrastive Learning for Likelihood-free Inference , 2020, ICML.

[172]  Erik Nijkamp,et al.  Learning Multi-layer Latent Variable Model via Variational Optimization of Short Run MCMC for Approximate Inference , 2019, ECCV.

[173]  Chris G. Willcocks,et al.  Gradient Origin Networks , 2020, ArXiv.

[174]  Ivan Kobyzev,et al.  Normalizing Flows: An Introduction and Review of Current Methods , 2020, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[175]  Ilya Sutskever,et al.  Zero-Shot Text-to-Image Generation , 2021, ICML.

[176]  Eduard H. Hovy,et al.  MAE: Mutual Posterior-Divergence Regularization for Variational AutoEncoders , 2019, ICLR.

[177]  Pascal Vincent,et al.  A Connection Between Score Matching and Denoising Autoencoders , 2011, Neural Computation.

[178]  Navdeep Jaitly,et al.  Adversarial Autoencoders , 2015, ArXiv.

[179]  Dustin Tran,et al.  Image Transformer , 2018, ICML.

[180]  François Chollet,et al.  Xception: Deep Learning with Depthwise Separable Convolutions , 2016, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[181]  Yoshua Bengio,et al.  Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling , 2014, ArXiv.

[182]  Achraf Oussidi,et al.  Deep generative models: Survey , 2018, 2018 International Conference on Intelligent Systems and Computer Vision (ISCV).

[183]  Prafulla Dhariwal,et al.  Glow: Generative Flow with Invertible 1x1 Convolutions , 2018, NeurIPS.

[184]  Alex Graves,et al.  Conditional Image Generation with PixelCNN Decoders , 2016, NIPS.

[185]  Ali Razavi,et al.  Generating Diverse High-Fidelity Images with VQ-VAE-2 , 2019, NeurIPS.

[186]  Mario Lucic,et al.  Are GANs Created Equal? A Large-Scale Study , 2017, NeurIPS.

[187]  Stefano Ermon,et al.  Towards Deeper Understanding of Variational Autoencoding Models , 2017, ArXiv.

[188]  Miguel Á. Carreira-Perpiñán,et al.  On Contrastive Divergence Learning , 2005, AISTATS.

[189]  Lantao Yu,et al.  Autoregressive Score Matching , 2020, NeurIPS.

[190]  Tie-Yan Liu,et al.  Discriminator Contrastive Divergence: Semi-Amortized Generative Modeling by Exploring Energy of the Discriminator , 2020, ArXiv.

[191]  Mohammad Norouzi,et al.  Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One , 2019, ICLR.

[192]  Matthias Bethge,et al.  A note on the evaluation of generative models , 2015, ICLR.

[193]  Samy Bengio,et al.  Generating Sentences from a Continuous Space , 2015, CoNLL.

[194]  Sebastian Nowozin,et al.  f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization , 2016, NIPS.

[195]  Nina Narodytska,et al.  RelGAN: Relational Generative Adversarial Networks for Text Generation , 2019, ICLR.

[196]  David J. Fleet,et al.  Exemplar VAE: Linking Generative Models, Nearest Neighbor Retrieval, and Data Augmentation , 2020, NeurIPS.

[197]  Jun Zhu,et al.  Implicit Normalizing Flows , 2021, ICLR.

[198]  Yizhe Zhu,et al.  Towards Faster and Stabilized GAN Training for High-fidelity Few-shot Image Synthesis , 2021, ICLR.

[199]  Ferenc Huszar,et al.  How (not) to Train your Generative Model: Scheduled Sampling, Likelihood, Adversary? , 2015, ArXiv.

[200]  Dimitris N. Metaxas,et al.  StackGAN: Text to Photo-Realistic Image Synthesis with Stacked Generative Adversarial Networks , 2016, 2017 IEEE International Conference on Computer Vision (ICCV).

[201]  Geoffrey E. Hinton,et al.  OPTIMAL PERCEPTUAL INFERENCE , 1983 .

[202]  Bernhard Pfahringer,et al.  Regularisation of neural networks by enforcing Lipschitz continuity , 2018, Machine Learning.

[203]  Max Welling,et al.  Improved Variational Inference with Inverse Autoregressive Flow , 2016, NIPS 2016.

[204]  Jonathon Shlens,et al.  Conditional Image Synthesis with Auxiliary Classifier GANs , 2016, ICML.

[205]  John E. Hopcroft,et al.  Stacked Generative Adversarial Networks , 2016, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[206]  Patrick Esser,et al.  Taming Transformers for High-Resolution Image Synthesis , 2021, 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[207]  Iain Murray,et al.  Masked Autoregressive Flow for Density Estimation , 2017, NIPS.

[208]  Heiga Zen,et al.  WaveNet: A Generative Model for Raw Audio , 2016, SSW.

[209]  Yoshua Bengio,et al.  Maximum Entropy Generators for Energy-Based Models , 2019, ArXiv.

[210]  Ngai-Man Cheung,et al.  Self-supervised GAN: Analysis and Improvement with Multi-class Minimax Game , 2019, NeurIPS.

[211]  Zengyi Li,et al.  A Neural Network MCMC Sampler That Maximizes Proposal Entropy , 2020, Entropy.

[212]  Yoshua Bengio,et al.  Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation , 2013, ArXiv.

[213]  E Weinan,et al.  Monge-Ampère Flow for Generative Modeling , 2018, ArXiv.

[214]  Maxim Raginsky,et al.  Theoretical guarantees for sampling and inference in generative models with latent diffusions , 2019, COLT.

[215]  Arthur Gretton,et al.  Generalized Energy Based Models , 2020, ICLR.

[216]  Andrew M. Dai,et al.  Flow Contrastive Estimation of Energy-Based Models , 2020, 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR).

[217]  Eduard H. Hovy,et al.  MaCow: Masked Convolutional Generative Flow , 2019, NeurIPS.

[218]  Anthony L. Caterini,et al.  Relaxing Bijectivity Constraints with Continuously Indexed Normalising Flows , 2019, ICML.