mlsanityData to 7 Oct 2026

An Introduction to Deep Generative Modeling

arXiv 2103.05180 ↗First posted 9 Mar 2021cs.LGcited by 104

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Abstract (arXiv)

Deep generative models (DGM) are neural networks with many hidden layers trained to approximate complicated, high-dimensional probability distributions using a large number of samples. When trained successfully, we can use the DGMs to estimate the likelihood of each observation and to create new samples from the underlying distribution. Developing DGMs has become one of the most hotly researched fields in artificial intelligence in recent years. The literature on DGMs has become vast and is growing rapidly. Some advances have even reached the public sphere, for example, the recent successes in generating realistic-looking images, voices, or movies; so-called deep fakes. Despite these successes, several mathematical and practical issues limit the broader use of DGMs: given a specific dataset, it remains challenging to design and train a DGM and even more challenging to find out why a particular model is or is not effective. To help advance the theoretical understanding of DGMs, we introduce DGMs and provide a concise mathematical framework for modeling the three most popular approaches: normalizing flows (NF), variational autoencoders (VAE), and generative adversarial networks (GAN). We illustrate the advantages and disadvantages of these basic approaches using numerical experiments. Our goal is to enable and motivate the reader to contribute to this proliferating research area. Our presentation also emphasizes relations between generative modeling and optimal transport.

Key facts. Cited by 104 papers in the map (data through 7 Oct 2026). Builds on 32 of its 55 references that are in the map. First posted on arXiv 9 Mar 2021.

Builds on

32 of 55 references.

References · 32

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
  3. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  4. 2013Auto-Encoding Variational Bayescited by 3,980
  5. 2016Improved Techniques for Training GANscited by 2,938
  6. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,609
  7. 2017Improved Training of Wasserstein GANscited by 2,223
  8. 2015Variational Inference with Normalizing Flowscited by 2,161
  9. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,048
  10. 2016Density estimation using Real NVPcited by 2,029
  11. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
  12. 2016Optimization Methods for Large-Scale Machine Learningcited by 1,140
20 more
  1. 2014NICE: Non-linear Independent Components Estimationcited by 1,052
  2. 2019An Introduction to Variational Autoencoderscited by 997
  3. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  4. 2016Improving Variational Inference with Inverse Autoregressive Flowcited by 636
  5. 2017Wasserstein GANcited by 635
  6. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  7. 2017Towards Principled Methods for Training Generative Adversarial Networkscited by 460
  8. 2016NIPS 2016 Tutorial: Generative Adversarial Networkscited by 284
  9. 2017Are GANs Created Equal? A Large-Scale Studycited by 267
  10. 2018Analyzing Inverse Problems with Invertible Neural Networkscited by 239
  11. 2020How to train your neural ODE: the world of Jacobian and kinetic regularizationcited by 228
  12. 2018A Variational Inequality Perspective on Generative Adversarial Networkscited by 144
  13. 2020OT-Flow: Fast and Accurate Continuous Normalizing Flows via Optimal Transportcited by 143
  14. 2019A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problemscited by 95
  15. 2018Monge-Amp`ere Flow for Generative Modelingcited by 33
  16. 2021Wasserstein GANs Work Because They Fail (to Approximate the Wasserstein Distance)cited by 33
  17. 2019MadMiner: Machine learning-based inference for particle physicscited by 32
  18. 2019Potential Flow Generator with L2 Optimal Transport Regularity for Generative Modelscited by 31
  19. 2020Stabilizing Invertible Neural Networks Using Mixture Modelscited by 30
  20. 2019Fluid Flow Mass Transport for Generative Networkscited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 10; 2022: 21; 2023: 20; 2024: 27; 2025: 17; 2026: 9.

104 papers.

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  1. 2021JFB: Jacobian-Free Backpropagation for Implicit Networkscited by 84
  2. 2023KL Convergence Guarantees for Score diffusion models under minimal data assumptionscited by 61
  3. 2023Geometry-Complete Diffusion for 3D Molecule Generation and Optimizationcited by 36
  4. 2021Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpointcited by 32
  5. 2021Generalized Normalizing Flows via Markov Chainscited by 23
  6. 2022The Neural Process Family: Survey, Applications and Perspectivescited by 23
  7. 2021Regularising Inverse Problems with Generative Machine Learning Modelscited by 22
  8. 2022PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularizationcited by 22
  9. 2023Precipitation nowcasting with generative diffusion modelscited by 22
  10. 2022Multivariate Quantile Function Forecastercited by 19
  11. 2023Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inferencecited by 19
  12. 2021A deep generative model for probabilistic energy forecasting in power systems: normalizing flowscited by 18
38 more
  1. 2021Unsupervised Deep Learning Methods for Biological Image Reconstruction and Enhancementcited by 17
  2. 2022Taming Hyperparameter Tuning in Continuous Normalizing Flows Using the JKO Schemecited by 17
  3. 2024PrefPaint: Aligning Image Inpainting Diffusion Model with Human Preferencecited by 17
  4. 2021On Learning the Transformer Kernelcited by 14
  5. 2022medigan: a Python library of pretrained generative models for medical image synthesiscited by 14
  6. 2022Generative modeling via tensor train sketchingcited by 13
  7. 2022Comparing the latent space of generative modelscited by 11
  8. 2022Generalization Metrics for Practical Quantum Advantage in Generative Modelscited by 8
  9. 2022Training Discrete Deep Generative Models via Gapped Straight-Through Estimatorcited by 8
  10. 2023Amortized Normalizing Flows for Transcranial Ultrasound with Uncertainty Quantificationcited by 8
  11. 2023Expressive variational quantum circuits provide inherent privacy in federated learningcited by 8
  12. 2025Artificial Intelligence and Generative Models for Materials Discovery -- A Reviewcited by 8
  13. 2023A generative flow for conditional sampling via optimal transportcited by 7
  14. 2024Differential Equations for Continuous-Time Deep Learningcited by 7
  15. 2024PhonologyBench: Evaluating Phonological Skills of Large Language Modelscited by 7
  16. 2024Importance Corrected Neural JKO Samplingcited by 7
  17. 2024State-observation augmented diffusion model for nonlinear assimilation with unknown dynamicscited by 7
  18. 2024A Review of Human Emotion Synthesis Based on Generative Technologycited by 7
  19. 2022Continuous Generative Neural Networks: A Wavelet-Based Architecture in Function Spacescited by 6
  20. 2022Denoising diffusion probabilistic models for probabilistic energy forecastingcited by 6
  21. 2023Diffusion map particle systems for generative modelingcited by 6
  22. 2023Leveraging Variational Autoencoders for Parameterized MMSE Estimationcited by 6
  23. 2024Generative Assignment Flows for Representing and Learning Joint Distributions of Discrete Datacited by 6
  24. 2024Predicting Critical Heat Flux with Uncertainty Quantification and Domain Generalization Using Conditional Variational Autoencoders and Deep Neural Networkscited by 6
  25. 2024Multi-objective Deep Learning: Taxonomy and Survey of the State of the Artcited by 6
  26. 2024Go With the Flow: Fast Diffusion for Gaussian Mixture Modelscited by 5
  27. 2025Good Things Come in Pairs: Paired Autoencoders for Inverse Problemscited by 5
  28. 2022Overparameterization Improves StyleGAN Inversioncited by 4
  29. 2022Compressed Sensing MRI Reconstruction Regularized by VAEs with Structured Image Covariancecited by 4
  30. 2022GAN-based Tabular Data Generator for Constructing Synopsis in Approximate Query Processing: Challenges and Solutionscited by 4
  31. 2024Prompt Smells: An Omen for Undesirable Generative AI Outputscited by 4
  32. 2024A Domain Translation Framework with an Adversarial Denoising Diffusion Model to Generate Synthetic Datasets of Echocardiography Imagescited by 4
  33. 2024Weak Generative Sampler to Efficiently Sample Invariant Distribution of Stochastic Differential Equationcited by 4
  34. 2024Stable generative modeling using Schr"odinger bridgescited by 3
  35. 2024Transfer learning with generative models for object detection on limited datasetscited by 3
  36. 2024Deep Generative Domain Adaptation with Temporal Relation Knowledge for Cross-User Activity Recognitioncited by 3
  37. 2024Deep Generative Domain Adaptation with Temporal Attention for Cross-User Activity Recognitioncited by 3
  38. 2024Nonlinear denoising score matching for enhanced learning of structured distributionscited by 3

50 most cited of 104 All 104 (JSON)