mlsanityData to 7 Oct 2026

Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistent

arXiv 2302.09057 ↗First posted 17 Feb 2023cs.LG cs.AI cs.CVcited by 58

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Imperfect score-matching leads to a shift between the training and the sampling distribution of diffusion models. Due to the recursive nature of the generation process, errors in previous steps yield sampling iterates that drift away from the training distribution. Yet, the standard training objective via Denoising Score Matching (DSM) is only designed to optimize over non-drifted data. To train on drifted data, we propose to enforce a consistency property which states that predictions of the model on its own generated data are consistent across time. Theoretically, we show that if the score is learned perfectly on some non-drifted points (via DSM) and if the consistency property is enforced everywhere, then the score is learned accurately everywhere. Empirically we show that our novel training objective yields state-of-the-art results for conditional and unconditional generation in CIFAR-10 and baseline improvements in AFHQ and FFHQ. We open-source our code and models: https://github.com/giannisdaras/cdm

Key facts. Cited by 58 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 45 of its 57 references that are in the map. First posted on arXiv 17 Feb 2023.

Builds on

45 of 57 references.

Closest ancestors · 21

Same direction, newest first

  1. 2022On Investigating the Conservative Property of Score-Based Generative Models26 Sep
  2. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  3. 2022Blurring Diffusion Models12 Sep
  4. 2022Soft Diffusion: Score Matching for General Corruptions12 Sep
  5. 2022Understanding Diffusion Models: A Unified Perspective25 Aug
  6. 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise19 Aug
  7. 2022Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning8 Aug
  8. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  9. 2022Generating High Fidelity Data from Low-density Regions using Diffusion Models31 Mar
  10. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  11. 2021Heavy-tailed denoising score matching17 Dec
  12. 2021Denoising Diffusion Gamma Models10 Oct
9 more
  1. 2021Variational Diffusion Models1 Jul
  2. 2021Soft Truncation: A Universal Training Technique of Score-based Diffusion Model for High Precision Score Estimation10 Jun
  3. 2021Gotta Go Fast When Generating Data with Score-Based Models28 May
  4. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  5. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  6. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  7. 2020Denoising Diffusion Implicit Models6 Oct
  8. 2020Denoising Diffusion Probabilistic Models19 Jun
  9. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 24

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  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. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  6. 2019Analyzing and Improving the Image Quality of StyleGANcited by 3,580
  7. 2022DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generationcited by 3,286
  8. 2022DreamFusion: Text-to-3D using 2D Diffusioncited by 3,006
  9. 2022Video Diffusion Modelscited by 2,280
  10. 2022An Image is Worth One Word: Personalizing Text-to-Image Generation using Textual Inversioncited by 2,231
  11. 2022Imagen Video: High Definition Video Generation with Diffusion Modelscited by 1,765
  12. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
12 more
  1. 2021Alias-Free Generative Adversarial Networkscited by 1,181
  2. 2022CogVideo: Large-scale Pretraining for Text-to-Video Generation via Transformerscited by 973
  3. 2020PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Modelscited by 358
  4. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
  5. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  6. 2022Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problemcited by 229
  7. 2022Structure-based Drug Design with Equivariant Diffusion Modelscited by 213
  8. 2021Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Imagescited by 110
  9. 2022Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Modelscited by 97
  10. 2021Estimating High Order Gradients of the Data Distribution by Denoisingcited by 63
  11. 2022Multiresolution Textual Inversioncited by 33
  12. 2022Score-Guided Intermediate Layer Optimization: Fast Langevin Mixing for Inverse Problemscited by 11

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 14; 2024: 15; 2025: 19; 2026: 10.

58 papers.

Sort:

By area:

  1. 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusioncited by 448
  2. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  3. 2023DDP: Diffusion Model for Dense Visual Predictioncited by 148
  4. 2023Ambient Diffusion: Learning Clean Distributions from Corrupted Datacited by 108
  5. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency modelscited by 99
  6. 2023Fast ODE-based Sampling for Diffusion Models in Around 5 Stepscited by 83
  7. 2024Distillation of Discrete Diffusion through Dimensional Correlationscited by 46
  8. 2023CoMoSpeech: One-Step Speech and Singing Voice Synthesis via Consistency Modelcited by 44
  9. 2024Consistent Diffusion Meets Tweedie: Training Exact Ambient Diffusion Models with Noisy Datacited by 44
  10. 2023The Journey, Not the Destination: How Data Guides Diffusion Modelscited by 42
  11. 2023DiffusionShield: A Watermark for Copyright Protection against Generative Diffusion Modelscited by 41
  12. 2023Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Datacited by 40
38 more
  1. 2024Autoregressive Models in Vision: A Surveycited by 39
  2. 2024Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Datacited by 32
  3. 2024Simple and Fast Distillation of Diffusion Modelscited by 31
  4. 2023On Error Propagation of Diffusion Modelscited by 30
  5. 2024VideoAgent: Self-Improving Video Generationcited by 24
  6. 2025Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Modelscited by 23
  7. 2024How much is a noisy image worth? Data Scaling Laws for Ambient Diffusioncited by 18
  8. 2025Ambient Diffusion Omni: Training Good Models with Bad Datacited by 18
  9. 2025Does Generation Require Memorization? Creative Diffusion Models using Ambient Diffusioncited by 17
  10. 2025Diffusion models for inverse problemscited by 15
  11. 2025FlexiDiT: Your Diffusion Transformer Can Easily Generate High-Quality Samples with Less Computecited by 12
  12. 2023Diffusion for Natural Image Mattingcited by 11
  13. 2024Structure-Guided Adversarial Training of Diffusion Modelscited by 11
  14. 2025Stochastic Forward-Backward Deconvolution: Training Diffusion Models with Finite Noisy Datasetscited by 11
  15. 2023On the Equivalence of Consistency-Type Models: Consistency Models, Consistent Diffusion Models, and Fokker-Planck Regularizationcited by 10
  16. 2023Synthetic Shifts to Initial Seed Vector Exposes the Brittle Nature of Latent-Based Diffusion Modelscited by 9
  17. 2024Neural Approximate Mirror Maps for Constrained Diffusion Modelscited by 7
  18. 2025Measurement Score-Based Diffusion Modelcited by 7
  19. 2024Generate and Instantiate What You Prefer: Text-Guided Diffusion for Sequential Recommendationcited by 6
  20. 2025DMQ: Dissecting Outliers of Diffusion Models for Post-Training Quantizationcited by 6
  21. 2025DiffEM: Learning from Corrupted Data with Diffusion Models via Expectation Maximizationcited by 6
  22. 2025X-Diffusion: Training Diffusion Policies on Cross-Embodiment Human Demonstrationscited by 6
  23. 2026Reinforcing Few-step Generators via Reward-Tilted Distribution Matchingcited by 6
  24. 2023ACT-Diffusion: Efficient Adversarial Consistency Training for One-step Diffusion Modelscited by 5
  25. 2026Exposure Bias Can Alleviate Itself via Directional and Frequency Rectification in Flow Matchingcited by 4
  26. 2024Physical Consistency Bridges Heterogeneous Data in Molecular Multi-Task Learningcited by 3
  27. 2025WAVE: Warp-Based View Guidance for Consistent Novel View Synthesis Using a Single Imagecited by 3
  28. 2026MMD Guidance: Training-Free Distribution Adaptation for Diffusion Models via Maximum Mean Discrepancy Guidancecited by 3
  29. 2024Suppress Content Shift: Better Diffusion Features via Off-the-Shelf Generation Techniquescited by 2
  30. 2025Multi-Step Consistency Models: Fast Generation with Theoretical Guaranteescited by 2
  31. 2025Constrained Diffusion Models for Synthesizing Representative Power Flow Datasetscited by 2
  32. 2025DEFT-VTON: Efficient Virtual Try-On with Consistent Generalised H-Transformcited by 2
  33. 2026FastDiSS: Few-step Match Many-step Diffusion Language Model on Sequence-to-Sequence Generation--Full Versioncited by 2
  34. 2023Multi-GradSpeech: Towards Diffusion-based Multi-Speaker Text-to-speech Using Consistent Diffusion Modelscited by 1
  35. 2025SFBD Flow: A Continuous-Optimization Framework for Training Diffusion Models with Noisy Samplescited by 1
  36. 2025Is Your Conditional Diffusion Model Actually Denoising?cited by 1
  37. 2026ASV3D: Adapting Diffusion-Based Single-View 3D Reconstruction with Extra Imagerycited by 1
  38. 2024Multi-Sensor Diffusion-Driven Optical Image Translation for Large-Scale Applicationscited by 0

50 most cited of 58 All 58 (JSON)

Similar, not cited

Close in wording, no citation either way

  1. 2024Towards a mathematical theory for consistency training in diffusion models
  2. 2024Truncated Consistency Models
  3. 2023Stable Target Field for Reduced Variance Score Estimation in Diffusion Models
  4. 2024Stable Consistency Tuning: Understanding and Improving Consistency Models
  5. 2025Implicit Regularisation in Diffusion Models: An Algorithm-Dependent Generalisation Analysis
  6. 2026Consistent Diffusion Language Models
  7. 2026Quantifying Error Propagation and Model Collapse in Diffusion Models
  8. 2025Convergence Of Consistency Model With Multistep Sampling Under General Data Assumptions