mlsanityData to 7 Oct 2026

Improved Denoising Diffusion Probabilistic Models

arXiv 2102.09672 ↗First posted 18 Feb 2021cs.LG cs.AI stat.MLcited by 3,736

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Denoising diffusion probabilistic models (DDPM) are a class of generative models which have recently been shown to produce excellent samples. We show that with a few simple modifications, DDPMs can also achieve competitive log-likelihoods while maintaining high sample quality. Additionally, we find that learning variances of the reverse diffusion process allows sampling with an order of magnitude fewer forward passes with a negligible difference in sample quality, which is important for the practical deployment of these models. We additionally use precision and recall to compare how well DDPMs and GANs cover the target distribution. Finally, we show that the sample quality and likelihood of these models scale smoothly with model capacity and training compute, making them easily scalable. We release our code at https://github.com/openai/improved-diffusion

Key facts. Cited by 3,736 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 39 of its 48 references that are in the map. First posted on arXiv 18 Feb 2021.

Builds on

39 of 48 references.

Closest ancestors · 4

Same direction, newest first

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  2. 2020Denoising Diffusion Implicit Models6 Oct
  3. 2020Denoising Diffusion Probabilistic Models19 Jun
  4. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 35

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  2. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  3. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  4. 2020Language Models are Few-Shot Learnerscited by 32,199
  5. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
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  10. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,609
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  12. 2019Generating Long Sequences with Sparse Transformerscited by 1,523
23 more
  1. 2019Generating Diverse High-Fidelity Images with VQ-VAE-2cited by 1,376
  2. 2015LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loopcited by 1,350
  3. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  4. 2019Improved Precision and Recall Metric for Assessing Generative Modelscited by 925
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  6. 2016Pixel Recurrent Neural Networkscited by 814
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  17. 2019Classification Accuracy Score for Conditional Generative Modelscited by 134
  18. 2020Learning Energy-Based Models by Diffusion Recovery Likelihoodcited by 122
  19. 2020Adversarial score matching and improved sampling for image generationcited by 95
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 61; 2022: 286; 2023: 920; 2024: 1032; 2025: 883; 2026: 554.

3,736 papers.

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  1. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  2. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  3. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  4. 2022Scalable Diffusion Models with Transformerscited by 5,931
  5. 2022Classifier-Free Diffusion Guidancecited by 5,717
  6. 2022Generative Adversarial Networkscited by 5,603
  7. 2023Adding Conditional Control to Text-to-Image Diffusion Modelscited by 5,466
  8. 2022Flow Matching for Generative Modelingcited by 5,426
  9. 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesiscited by 4,094
  10. 2021GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Modelscited by 3,595
  11. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  12. 2022DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generationcited by 3,286
38 more
  1. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  2. 2022Video Diffusion Modelscited by 2,280
  3. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,961
  4. 2022Imagen Video: High Definition Video Generation with Diffusion Modelscited by 1,765
  5. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,665
  6. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  7. 2023Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Modelscited by 1,465
  8. 2024Octo: An Open-Source Generalist Robot Policycited by 1,427
  9. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,419
  10. 2021Palette: Image-to-Image Diffusion Modelscited by 1,296
  11. 2021Cascaded Diffusion Models for High Fidelity Image Generationcited by 1,155
  12. 2021Variational Diffusion Modelscited by 1,145
  13. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  14. 2022MaskGIT: Masked Generative Image Transformercited by 1,082
  15. 2022Planning with Diffusion for Flexible Behavior Synthesiscited by 1,023
  16. 2022Diffusion Models in Vision: A Surveycited by 1,008
  17. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,006
  18. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  19. 2022Denoising Diffusion Restoration Modelscited by 951
  20. 2023Training Diffusion Models with Reinforcement Learningcited by 939
  21. 2021Blended Diffusion for Text-driven Editing of Natural Imagescited by 924
  22. 2022DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Modelscited by 924
  23. 2023PixArt-α: Fast Training of Diffusion Transformer for Photorealistic Text-to-Image Synthesiscited by 854
  24. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  25. 2023Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inferencecited by 826
  26. 2021Vector Quantized Diffusion Model for Text-to-Image Synthesiscited by 773
  27. 2022MotionDiffuse: Text-Driven Human Motion Generation with Diffusion Modelcited by 768
  28. 2023Extracting Training Data from Diffusion Modelscited by 723
  29. 2023MasaCtrl: Tuning-Free Mutual Self-Attention Control for Consistent Image Synthesis and Editingcited by 722
  30. 2022On Distillation of Guided Diffusion Modelscited by 721
  31. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformerscited by 707
  32. 2022Pseudo Numerical Methods for Diffusion Models on Manifoldscited by 695
  33. 2022Point-E: A System for Generating 3D Point Clouds from Complex Promptscited by 694
  34. 2024RDT-1B: a Diffusion Foundation Model for Bimanual Manipulationcited by 670
  35. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  36. 2024Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Thinkcited by 666
  37. 2021Vector-quantized Image Modeling with Improved VQGANcited by 656
  38. 2024Autoregressive Image Generation without Vector Quantizationcited by 644

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  4. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions
  5. 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
  6. 2023To smooth a cloud or to pin it down: Guarantees and Insights on Score Matching in Denoising Diffusion Models
  7. 2025Improved Diffusion-based Generative Model with Better Adversarial Robustness
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