mlsanityData to 7 Oct 2026

Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion

arXiv 2310.02279 ↗First posted 1 Oct 2023cs.LG cs.AI cs.CVcited by 448

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Consistency Models (CM) (Song et al., 2023) accelerate score-based diffusion model sampling at the cost of sample quality but lack a natural way to trade-off quality for speed. To address this limitation, we propose Consistency Trajectory Model (CTM), a generalization encompassing CM and score-based models as special cases. CTM trains a single neural network that can -- in a single forward pass -- output scores (i.e., gradients of log-density) and enables unrestricted traversal between any initial and final time along the Probability Flow Ordinary Differential Equation (ODE) in a diffusion process. CTM enables the efficient combination of adversarial training and denoising score matching loss to enhance performance and achieves new state-of-the-art FIDs for single-step diffusion model sampling on CIFAR-10 (FID 1.73) and ImageNet at 64x64 resolution (FID 1.92). CTM also enables a new family of sampling schemes, both deterministic and stochastic, involving long jumps along the ODE solution trajectories. It consistently improves sample quality as computational budgets increase, avoiding the degradation seen in CM. Furthermore, unlike CM, CTM's access to the score function can streamline the adoption of established controllable/conditional generation methods from the diffusion community. This access also enables the computation of likelihood. The code is available at https://github.com/sony/ctm.

Key facts. Cited by 448 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 58 of its 87 references that are in the map. First posted on arXiv 1 Oct 2023.

Builds on

58 of 87 references.

Closest ancestors · 29

Same direction, newest first

  1. 2023Restart Sampling for Improving Generative Processes26 Jun
  2. 2023BOOT: Data-free Distillation of Denoising Diffusion Models with Bootstrapping8 Jun
  3. 2023On the Equivalence of Consistency-Type Models: Consistency Models, Consistent Diffusion Models, and Fokker-Planck Regularization1 Jun
  4. 2023TRACT: Denoising Diffusion Models with Transitive Closure Time-Distillation7 Mar
  5. 2023Consistency Models2 Mar
  6. 2023Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistent17 Feb
  7. 2022Refining Generative Process with Discriminator Guidance in Score-based Diffusion Models28 Nov
  8. 2022Fast Sampling of Diffusion Models via Operator Learning24 Nov
  9. 2022FP-Diffusion: Improving Score-based Diffusion Models by Enforcing the Underlying Score Fokker-Planck Equation9 Oct
  10. 2022On Distillation of Guided Diffusion Models6 Oct
  11. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  12. 2022Classifier-Free Diffusion Guidance26 Jul
17 more
  1. 2022Maximum Likelihood Training for Score-Based Diffusion ODEs by High-Order Denoising Score Matching16 Jun
  2. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  3. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  4. 2022Maximum Likelihood Training of Implicit Nonlinear Diffusion Models27 May
  5. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  6. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  7. 2021Variational Diffusion Models1 Jul
  8. 2021Score-based Generative Modeling in Latent Space10 Jun
  9. 2021Soft Truncation: A Universal Training Technique of Score-based Diffusion Model for High Precision Score Estimation10 Jun
  10. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  11. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  12. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  13. 2021Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed7 Jan
  14. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  15. 2020Denoising Diffusion Implicit Models6 Oct
  16. 2020Denoising Diffusion Probabilistic Models19 Jun
  17. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 29

  1. 2017Attention Is All You Needcited by 59,932
  2. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,029
  3. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,441
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  5. 2019EfficientNet: Rethinking Model Scaling for Convolutional Neural Networkscited by 6,415
  6. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  7. 2020Training data-efficient image transformers & distillation through attentioncited by 4,560
  8. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  9. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  10. 2020Taming Transformers for High-Resolution Image Synthesiscited by 3,229
  11. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,609
  12. 2021Palette: Image-to-Image Diffusion Modelscited by 1,296
17 more
  1. 2020Training Generative Adversarial Networks with Limited Datacited by 1,184
  2. 2019StarGAN v2: Diverse Image Synthesis for Multiple Domainscited by 1,095
  3. 2022Denoising Diffusion Restoration Modelscited by 951
  4. 2016f-GAN: Training Generative Neural Samplers using Variational Divergence Minimizationcited by 504
  5. 2022StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasetscited by 489
  6. 2022The Role of ImageNet Classes in Fr'echet Inception Distancecited by 211
  7. 2023Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restorationcited by 164
  8. 2023GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restorationcited by 58
  9. 2021Rebooting ACGAN: Auxiliary Classifier GANs with Stable Trainingcited by 57
  10. 2022Unsupervised vocal dereverberation with diffusion-based generative modelscited by 18
  11. 2020Implicit Kernel Attentioncited by 13
  12. 2022DiffRoll: Diffusion-based Generative Music Transcription with Unsupervised Pretraining Capabilitycited by 13
  13. 2023Catch-Up Distillation: You Only Need to Train Once for Accelerating Samplingcited by 13
  14. 2023VRDMG: Vocal Restoration via Diffusion Posterior Sampling with Multiple Guidancecited by 9
  15. 2020Adversarial Likelihood-Free Inference on Black-Box Generatorcited by 3
  16. 2020Sequential Likelihood-Free Inference with Neural Proposalcited by 1
  17. 2022Automatic Calibration Framework of Agent-Based Models for Dynamic and Heterogeneous Parameterscited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 9; 2024: 124; 2025: 169; 2026: 146.

448 papers.

Sort:

By area:

  1. 2023Adversarial Diffusion Distillationcited by 741
  2. 2024Improved Distribution Matching Distillation for Fast Image Synthesiscited by 648
  3. 2025Mean Flows for One-step Generative Modelingcited by 524
  4. 2024From Slow Bidirectional to Fast Autoregressive Video Diffusion Modelscited by 401
  5. 2024Simplifying, Stabilizing and Scaling Continuous-Time Consistency Modelscited by 276
  6. 2024SDXL-Lightning: Progressive Adversarial Diffusion Distillationcited by 258
  7. 2024Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generationcited by 211
  8. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  9. 2024Hyper-SD: Trajectory Segmented Consistency Model for Efficient Image Synthesiscited by 153
  10. 2024Consistency Models Made Easycited by 140
  11. 2024Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-Based Decodingcited by 127
  12. 2025Fast Video Generation with Sliding Tile Attentioncited by 123
38 more
  1. 2024ReNO: Enhancing One-step Text-to-Image Models through Reward-based Noise Optimizationcited by 115
  2. 2025Inductive Moment Matchingcited by 107
  3. 2024Improving the Training of Rectified Flowscited by 106
  4. 2025Improved Mean Flows: On the Challenges of Fastforward Generative Modelscited by 102
  5. 2024Consistency Flow Matching: Defining Straight Flows with Velocity Consistencycited by 101
  6. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency modelscited by 99
  7. 2025How to build a consistency model: Learning flow maps via self-distillationcited by 96
  8. 2024Align Your Steps: Optimizing Sampling Schedules in Diffusion Modelscited by 91
  9. 2025SANA-Sprint: One-Step Diffusion with Continuous-Time Consistency Distillationcited by 85
  10. 2024Phased Consistency Modelscited by 83
  11. 2024One-Step Diffusion Policy: Fast Visuomotor Policies via Diffusion Distillationcited by 83
  12. 2025Align Your Flow: Scaling Continuous-Time Flow Map Distillationcited by 81
  13. 2025Large Scale Diffusion Distillation via Score-Regularized Continuous-Time Consistencycited by 81
  14. 2024Distilling Diffusion Models into Conditional GANscited by 78
  15. 2024Multistep Distillation of Diffusion Models via Moment Matchingcited by 76
  16. 2024Simpler Diffusion (SiD2): 1.5 FID on ImageNet512 with pixel-space diffusioncited by 74
  17. 2024DITTO: Diffusion Inference-Time T-Optimization for Music Generationcited by 73
  18. 2025Yume: An Interactive World Generation Modelcited by 73
  19. 2024One-Step Diffusion Distillation through Score Implicit Matchingcited by 68
  20. 2024Multistep Consistency Modelscited by 67
  21. 2024Accelerating Auto-regressive Text-to-Image Generation with Training-free Speculative Jacobi Decodingcited by 65
  22. 2024TurboEdit: Text-Based Image Editing Using Few-Step Diffusion Modelscited by 64
  23. 2024Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorialcited by 60
  24. 2024EM Distillation for One-step Diffusion Modelscited by 60
  25. 2024Flash Diffusion: Accelerating Any Conditional Diffusion Model for Few Steps Image Generationcited by 56
  26. 2023CoCoGen: Physically-Consistent and Conditioned Score-based Generative Models for Forward and Inverse Problemscited by 54
  27. 2024Streaming Diffusion Policy: Fast Policy Synthesis with Variable Noise Diffusion Modelscited by 51
  28. 2024Adversarial Diffusion Compression for Real-World Image Super-Resolutioncited by 49
  29. 2025Learning Few-Step Diffusion Models by Trajectory Distribution Matchingcited by 49
  30. 2026One-step Latent-free Image Generation with Pixel Mean Flowscited by 49
  31. 2024LCM-Lookahead for Encoder-based Text-to-Image Personalizationcited by 48
  32. 2024AnimateDiff-Lightning: Cross-Model Diffusion Distillationcited by 47
  33. 2024Diffusion Bridge Implicit Modelscited by 47
  34. 2024Adversarial Score identity Distillation: Rapidly Surpassing the Teacher in One Stepcited by 47
  35. 2024Distillation of Discrete Diffusion through Dimensional Correlationscited by 46
  36. 2024Trajectory Consistency Distillation: Improved Latent Consistency Distillation by Semi-Linear Consistency Function with Trajectory Mappingcited by 44
  37. 2025One-step Diffusion Models with f-Divergence Distribution Matchingcited by 43
  38. 2024LinFusion: 1 GPU, 1 Minute, 16K Imagecited by 42

50 most cited of 448 All 448 (JSON)

Similar, not cited

Close in wording, no citation either way

  1. 2024Improving Consistency Models with Generator-Augmented Flows
  2. 2023Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference
  3. 2025ETC: training-free diffusion models acceleration with Error-aware Trend Consistency
  4. 2023Stable Target Field for Reduced Variance Score Estimation in Diffusion Models
  5. 2026Consistent Diffusion Language Models
  6. 2025ODEt(ODEl): Shortcutting the Time and the Length in Diffusion and Flow Models for Faster Sampling
  7. 2026Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Sampling
  8. 2025Single-Step Consistent Diffusion Samplers