mlsanityData to 7 Oct 2026

Normalizing Flows are Capable Generative Models

arXiv 2412.06329 ↗First posted 9 Dec 2024cs.CV cs.LGcited by 89

Not on the map. Why?

Cited by 27 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Normalizing Flows (NFs) are likelihood-based models for continuous inputs. They have demonstrated promising results on both density estimation and generative modeling tasks, but have received relatively little attention in recent years. In this work, we demonstrate that NFs are more powerful than previously believed. We present TarFlow: a simple and scalable architecture that enables highly performant NF models. TarFlow can be thought of as a Transformer-based variant of Masked Autoregressive Flows (MAFs): it consists of a stack of autoregressive Transformer blocks on image patches, alternating the autoregression direction between layers. TarFlow is straightforward to train end-to-end, and capable of directly modeling and generating pixels. We also propose three key techniques to improve sample quality: Gaussian noise augmentation during training, a post training denoising procedure, and an effective guidance method for both class-conditional and unconditional settings. Putting these together, TarFlow sets new state-of-the-art results on likelihood estimation for images, beating the previous best methods by a large margin, and generates samples with quality and diversity comparable to diffusion models, for the first time with a stand-alone NF model. We make our code available at https://github.com/apple/ml-tarflow.

Key facts. Cited by 89 papers in the map (data through 7 Oct 2026). Builds on 55 of its 66 references that are in the map. First posted on arXiv 9 Dec 2024.

Builds on

55 of 66 references.

References · 55

  1. 2020Language Models are Few-Shot Learnerscited by 32,199
  2. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
  3. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  7. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  8. 2022Classifier-Free Diffusion Guidancecited by 5,717
  9. 2022Flow Matching for Generative Modelingcited by 5,426
  10. 2017Neural Discrete Representation Learningcited by 4,650
  11. 2023SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesiscited by 4,290
  12. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
38 more
  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2020Taming Transformers for High-Resolution Image Synthesiscited by 3,229
  3. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  4. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,609
  5. 2015Variational Inference with Normalizing Flowscited by 2,161
  6. 2016Density estimation using Real NVPcited by 2,029
  7. 2023Consistency Modelscited by 1,778
  8. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  9. 2019Generating Long Sequences with Sparse Transformerscited by 1,523
  10. 2019Generating Diverse High-Fidelity Images with VQ-VAE-2cited by 1,376
  11. 2022Scaling Autoregressive Models for Content-Rich Text-to-Image Generationcited by 1,287
  12. 2021Cascaded Diffusion Models for High Fidelity Image Generationcited by 1,155
  13. 2021Variational Diffusion Modelscited by 1,145
  14. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,095
  15. 2024Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Predictioncited by 1,005
  16. 2016Conditional Image Generation with PixelCNN Decoderscited by 859
  17. 2016Pixel Recurrent Neural Networkscited by 814
  18. 2024Autoregressive Model Beats Diffusion: Llama for Scalable Image Generationcited by 760
  19. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  20. 2024Autoregressive Image Generation without Vector Quantizationcited by 644
  21. 2016Improving Variational Inference with Inverse Autoregressive Flowcited by 636
  22. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  23. 2023Scaling up GANs for Text-to-Image Synthesiscited by 492
  24. 2023Improved Techniques for Training Consistency Modelscited by 430
  25. 2018Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Networkcited by 415
  26. 2023Simple diffusion: End-to-end diffusion for high resolution imagescited by 413
  27. 2019Augmented Neural ODEscited by 396
  28. 2015MADE: Masked Autoencoder for Distribution Estimationcited by 306
  29. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplingscited by 267
  30. 2020Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Imagescited by 261
  31. 2019Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Designcited by 258
  32. 2022Scalable Adaptive Computation for Iterative Generationcited by 190
  33. 2023GIVT: Generative Infinite-Vocabulary Transformerscited by 80
  34. 2018Generating High Fidelity Images with Subscale Pixel Networks and Multidimensional Upscalingcited by 74
  35. 2019Block Neural Autoregressive Flowcited by 62
  36. 2019Stabilizing Generative Adversarial Networks: A Surveycited by 57
  37. 2024JetFormer: An Autoregressive Generative Model of Raw Images and Textcited by 44
  38. 2024Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modellingcited by 43

50 most cited of 55 All 55 (JSON)

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 45; 2026: 43.

89 papers.

Sort:

By area:

  1. 2025Diffusion Transformers with Representation Autoencoderscited by 275
  2. 2026Generative Modeling via Driftingcited by 98
  3. 2025PixelFlow: Pixel-Space Generative Models with Flowcited by 91
  4. 2025PixNerd: Pixel Neural Field Diffusioncited by 75
  5. 2025DeCo: Frequency-Decoupled Pixel Diffusion for End-to-End Image Generationcited by 55
  6. 2025Fractal Generative Modelscited by 44
  7. 2025Scalable Equilibrium Sampling with Sequential Boltzmann Generatorscited by 36
  8. 2025Continuously Augmented Discrete Diffusion model for Categorical Generative Modelingcited by 32
  9. 2025STARFlow: Scaling Latent Normalizing Flows for High-resolution Image Synthesiscited by 31
  10. 2025One Layer Is Enough: Adapting Pretrained Visual Encoders for Image Generationcited by 27
  11. 2025Progressive Inference-Time Annealing of Diffusion Models for Sampling from Boltzmann Densitiescited by 26
  12. 2025Target Concrete Score Matching: A Holistic Framework for Discrete Diffusioncited by 25
38 more
  1. 2025Learning normalized image densities via dual score matchingcited by 17
  2. 2025FARMER: Flow AutoRegressive Transformer over Pixelscited by 17
  3. 2025Joint Distillation for Fast Likelihood Evaluation and Sampling in Flow-based Modelscited by 17
  4. 2025Temperature-Annealed Boltzmann Generatorscited by 14
  5. 2025Normalizing Flows are Capable Models for Continuous Controlcited by 13
  6. 2024Jet: A Modern Transformer-Based Normalizing Flowcited by 12
  7. 2025Ideas in Inference-time Scaling can Benefit Generative Pre-training Algorithmscited by 12
  8. 2025Amortized Sampling with Transferable Normalizing Flowscited by 11
  9. 2026PixelGen: Improving Pixel Diffusion with Perceptual Supervisioncited by 10
  10. 2025STARFlow-V: End-to-End Video Generative Modeling with Normalizing Flowscited by 9
  11. 2025Flexible Language Modeling in Continuous Space with Transformer-based Autoregressive Flowscited by 8
  12. 2025Learning Boltzmann Generators via Constrained Mass Transportcited by 8
  13. 2025Bidirectional Normalizing Flow: From Data to Noise and Backcited by 7
  14. 2025Efficient Regression-Based Training of Normalizing Flows for Boltzmann Generatorscited by 6
  15. 2025SimFlow: Simplified and End-to-End Training of Latent Normalizing Flowscited by 6
  16. 2026End-to-End Training for Unified Tokenization and Latent Denoisingcited by 6
  17. 2026PixelU: A U-Shaped Transformer for Efficient End-to-End Pixel Diffusioncited by 6
  18. 2025NinA: Normalizing Flows in Action. Training VLA Models with Normalizing Flowscited by 5
  19. 2025Calibrating Generative Models to Distributional Constraintscited by 5
  20. 2025REGLUE Your Latents with Global and Local Semantics for Entangled Diffusioncited by 5
  21. 2026Latent Reasoning with Normalizing Flowscited by 4
  22. 2025Multivariate Latent Recalibration for Conditional Normalizing Flowscited by 3
  23. 2025Flow Stochastic Segmentation Networkscited by 3
  24. 2026Normalizing Flows with Iterative Denoisingcited by 3
  25. 2026Explorative Modeling: Unlocking a Third Pretraining Axis and End-to-End Generationcited by 3
  26. 2025Accelerate TarFlow Sampling with GS-Jacobi Iterationcited by 2
  27. 2025Aligning Latent Spaces with Flow Priorscited by 2
  28. 2025Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulencecited by 2
  29. 2025Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutionscited by 2
  30. 2025Are Euler angles a useful rotation parameterisation for pose estimation with Normalizing Flows?cited by 2
  31. 2025Flowing Backwards: Improving Normalizing Flows via Reverse Representation Alignmentcited by 2
  32. 2025TARFVAE: Efficient One-Step Generative Time Series Forecasting via TARFLOW based VAEcited by 2
  33. 2026How well do generative models solve inverse problems? A benchmark studycited by 2
  34. 2026Efficient Training of Boltzmann Generators Using Off-Policy Log-Dispersion Regularizationcited by 2
  35. 2026Temporal Pair Consistency for Variance-Reduced Flow Matchingcited by 2
  36. 2026Preconditioned Flow Matchingcited by 2
  37. 2026The Coupling Within: Flow Matching via Distilled Normalizing Flowscited by 2
  38. 2026MPDiT: Multi-Patch Global-to-Local Transformer Architecture For Efficient Flow Matching and Diffusion Modelcited by 2

50 most cited of 89 All 89 (JSON)

Similar, not cited

Close in wording, no citation either way

  1. 2026Simplifying Flow Matching Transformations with Low-Rank Mixture Models
  2. 2025Decoupled MeanFlow: Turning Flow Models into Flow Maps for Accelerated Sampling
  3. 2021Diffusion Normalizing Flow
  4. 2023Diffusion Models with Deterministic Normalizing Flow Priors
  5. 2023Improving and generalizing flow-based generative models with minibatch optimal transport
  6. 2022Building Normalizing Flows with Stochastic Interpolants
  7. 2025Designing a Conditional Prior Distribution for Flow-Based Generative Models
  8. 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesis