mlsanityData to 14 Oct 2026

Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models

arXiv 2410.11081 ↗First posted 14 Oct 2024cs.LG stat.MLcited by 283

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Consistency models (CMs) are a powerful class of diffusion-based generative models optimized for fast sampling. Most existing CMs are trained using discretized timesteps, which introduce additional hyperparameters and are prone to discretization errors. While continuous-time formulations can mitigate these issues, their success has been limited by training instability. To address this, we propose a simplified theoretical framework that unifies previous parameterizations of diffusion models and CMs, identifying the root causes of instability. Based on this analysis, we introduce key improvements in diffusion process parameterization, network architecture, and training objectives. These changes enable us to train continuous-time CMs at an unprecedented scale, reaching 1.5B parameters on ImageNet 512x512. Our proposed training algorithm, using only two sampling steps, achieves FID scores of 2.06 on CIFAR-10, 1.48 on ImageNet 64x64, and 1.88 on ImageNet 512x512, narrowing the gap in FID scores with the best existing diffusion models to within 10%.

Key facts. Cited by 283 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 85 of its 92 references that are in the map. First posted on arXiv 14 Oct 2024.

Builds on

85 of 92 references.

Closest ancestors · 48

Same direction, newest first

  1. 2024Consistency Models Made Easy20 Jun
  2. 2024Alleviating Distortion in Image Generation via Multi-Resolution Diffusion Models and Time-Dependent Layer Normalization13 Jun
  3. 2024Multistep Distillation of Diffusion Models via Moment Matching6 Jun
  4. 2024EM Distillation for One-step Diffusion Models27 May
  5. 2024Improved Distribution Matching Distillation for Fast Image Synthesis23 May
  6. 2024U-DiTs: Downsample Tokens in U-Shaped Diffusion Transformers4 May
  7. 2024Diffusion-RWKV: Scaling RWKV-Like Architectures for Diffusion Models6 Apr
  8. 2024Score identity Distillation: Exponentially Fast Distillation of Pretrained Diffusion Models for One-Step Generation5 Apr
  9. 2024Multistep Consistency Models11 Mar
  10. 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesis5 Mar
  11. 2024Scalable Diffusion Models with State Space Backbone8 Feb
  12. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers16 Jan
36 more
  1. 2023Non-Denoising Forward-Time Diffusions22 Dec
  2. 2023Analyzing and Improving the Training Dynamics of Diffusion Models5 Dec
  3. 2023DiffiT: Diffusion Vision Transformers for Image Generation4 Dec
  4. 2023One-step Diffusion with Distribution Matching Distillation30 Nov
  5. 2023Diffusion Models Without Attention30 Nov
  6. 2023Adversarial Diffusion Distillation28 Nov
  7. 2023Improved Techniques for Training Consistency Models22 Oct
  8. 2023DPM-Solver-v3: Improved Diffusion ODE Solver with Empirical Model Statistics20 Oct
  9. 2023Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference6 Oct
  10. 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion1 Oct
  11. 2023Fast Training of Diffusion Models with Masked Transformers15 Jun
  12. 2023BOOT: Data-free Distillation of Denoising Diffusion Models with Bootstrapping8 Jun
  13. 2023Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Models29 May
  14. 2023Common Diffusion Noise Schedules and Sample Steps are Flawed15 May
  15. 2023Iterative α-(de)Blending: a Minimalist Deterministic Diffusion Model5 May
  16. 2023TRACT: Denoising Diffusion Models with Transitive Closure Time-Distillation7 Mar
  17. 2023Consistency Models2 Mar
  18. 2023Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation1 Mar
  19. 2023Simple diffusion: End-to-end diffusion for high resolution images26 Jan
  20. 2022Scalable Diffusion Models with Transformers19 Dec
  21. 2022Fast Sampling of Diffusion Models via Operator Learning24 Nov
  22. 2022DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models2 Nov
  23. 2022On Distillation of Guided Diffusion Models6 Oct
  24. 2022All are Worth Words: A ViT Backbone for Diffusion Models25 Sep
  25. 2022Classifier-Free Diffusion Guidance26 Jul
  26. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  27. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  28. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  29. 2021Tackling the Generative Learning Trilemma with Denoising Diffusion GANs15 Dec
  30. 2021Variational Diffusion Models1 Jul
  31. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  32. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  33. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  34. 2021Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed7 Jan
  35. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  36. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 37

  1. 2017Attention Is All You Needcited by 60,361
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  3. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,177
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  5. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  6. 2022Flow Matching for Generative Modelingcited by 5,702
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  8. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  9. 2022FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awarenesscited by 3,673
  10. 2020Taming Transformers for High-Resolution Image Synthesiscited by 3,253
  11. 2022DreamFusion: Text-to-3D using 2D Diffusioncited by 3,025
  12. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,988
25 more
  1. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,626
  2. 2023FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioningcited by 2,598
  3. 2023Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasetscited by 2,581
  4. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,200
  5. 2022Imagen Video: High Definition Video Generation with Diffusion Modelscited by 1,778
  6. 2023Zero-1-to-3: Zero-shot One Image to 3D Objectcited by 1,489
  7. 2023ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillationcited by 1,219
  8. 2022MaskGIT: Masked Generative Image Transformercited by 1,099
  9. 2022Planning with Diffusion for Flexible Behavior Synthesiscited by 1,061
  10. 2024Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Predictioncited by 1,023
  11. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  12. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  13. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 879
  14. 2018Multi-Task Learning as Multi-Objective Optimizationcited by 821
  15. 2019On the Variance of the Adaptive Learning Rate and Beyondcited by 772
  16. 2024Autoregressive Image Generation without Vector Quantizationcited by 651
  17. 2023Language Model Beats Diffusion -- Tokenizer is Key to Visual Generationcited by 640
  18. 2023AudioLDM: Text-to-Audio Generation with Latent Diffusion Modelscited by 599
  19. 2022StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasetscited by 492
  20. 2022Diffusion-GAN: Training GANs with Diffusioncited by 205
  21. 2022Scalable Adaptive Computation for Iterative Generationcited by 195
  22. 2024Fast Timing-Conditioned Latent Audio Diffusioncited by 181
  23. 2024Consistency Flow Matching: Defining Straight Flows with Velocity Consistencycited by 104
  24. 2024Optimal Flow Matching: Learning Straight Trajectories in Just One Stepcited by 78
  25. 2024DiM: Diffusion Mamba for Efficient High-Resolution Image Synthesiscited by 72

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 9; 2025: 117; 2026: 157.

283 papers.

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  1. 2025Mean Flows for One-step Generative Modelingcited by 561
  2. 2025World Simulation with Video Foundation Models for Physical AIcited by 200
  3. 2026Causal Forcing: Autoregressive Diffusion Distillation Done Right for High-Quality Real-Time Interactive Video Generationcited by 184
  4. 2025Diffusion Adversarial Post-Training for One-Step Video Generationcited by 151
  5. 2025Training Agents Inside of Scalable World Modelscited by 136
  6. 2025Inductive Moment Matchingcited by 113
  7. 2025Improved Mean Flows: On the Challenges of Fastforward Generative Modelscited by 110
  8. 2025How to build a consistency model: Learning flow maps via self-distillationcited by 103
  9. 2025Autoregressive Adversarial Post-Training for Real-Time Interactive Video Generationcited by 90
  10. 2025SANA-Sprint: One-Step Diffusion with Continuous-Time Consistency Distillationcited by 87
  11. 2025Align Your Flow: Scaling Continuous-Time Flow Map Distillationcited by 87
  12. 2025Large Scale Diffusion Distillation via Score-Regularized Continuous-Time Consistencycited by 86
38 more
  1. 2026LoopFormer: Elastic-Depth Looped Transformers for Latent Reasoning via Shortcut Modulationcited by 61
  2. 2025DiTAR: Diffusion Transformer Autoregressive Modeling for Speech Generationcited by 57
  3. 2024SoftVQ-VAE: Efficient 1-Dimensional Continuous Tokenizercited by 56
  4. 2026Causal Forcing++: Scalable Few-Step Autoregressive Diffusion Distillation for Real-Time Interactive Video Generationcited by 56
  5. 2026One-step Latent-free Image Generation with Pixel Mean Flowscited by 53
  6. 2025SeedVR2: One-Step Video Restoration via Diffusion Adversarial Post-Trainingcited by 50
  7. 2025Distribution Matching Distillation Meets Reinforcement Learningcited by 50
  8. 2024Adversarial Score identity Distillation: Rapidly Surpassing the Teacher in One Stepcited by 47
  9. 2025Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithmscited by 47
  10. 2025Decoupled DMD: CFG Augmentation as the Spear, Distribution Matching as the Shieldcited by 45
  11. 2026Categorical Flow Mapscited by 44
  12. 2025One-step Diffusion Models with f-Divergence Distribution Matchingcited by 43
  13. 2025Adversarial Distribution Matching for Diffusion Distillation Towards Efficient Image and Video Synthesiscited by 41
  14. 2025AlphaFlow: Understanding and Improving MeanFlow Modelscited by 41
  15. 2025Omni-Video: Democratizing Unified Video Understanding and Generationcited by 40
  16. 2026Representation Fr'echet Loss for Visual Generationcited by 37
  17. 2026Qwen-Image-2.0 Technical Reportcited by 36
  18. 2025Efficient Diffusion Models: A Surveycited by 35
  19. 2025Transition Models: Rethinking the Generative Learning Objectivecited by 34
  20. 2025SenseFlow: Scaling Distribution Matching for Flow-based Text-to-Image Distillationcited by 32
  21. 2025A Survey on Parallel Text Generation: From Parallel Decoding to Diffusion Language Modelscited by 30
  22. 2025StreamDiffusionV2: A Streaming System for Dynamic and Interactive Video Generationcited by 30
  23. 2026Transition Matching Distillation for Fast Video Generationcited by 30
  24. 2025VideoScene: Distilling Video Diffusion Model to Generate 3D Scenes in One Stepcited by 27
  25. 2024DOLLAR: Few-Step Video Generation via Distillation and Latent Reward Optimizationcited by 26
  26. 2025Unleashing Vecset Diffusion Model for Fast Shape Generationcited by 26
  27. 2025SplitMeanFlow: Interval Splitting Consistency in Few-Step Generative Modelingcited by 26
  28. 2026AnyFlow: Any-Step Video Diffusion Model with On-Policy Flow Map Distillationcited by 26
  29. 2025Investigating Text Insulation and Attention Mechanisms for Complex Visual Text Generationcited by 25
  30. 2026Causal-rCM: A Unified Teacher-Forcing and Self-Forcing Open Recipe for Autoregressive Diffusion Distillation in Streaming Video Generation and Interactive World Modelscited by 25
  31. 2026One-Step Generative Modeling via Wasserstein Gradient Flowscited by 24
  32. 2025Dual-Expert Consistency Model for Efficient and High-Quality Video Generationcited by 21
  33. 2025Playing with Transformer at 30+ FPS via Next-Frame Diffusioncited by 20
  34. 2025Decoupled MeanFlow: Turning Flow Models into Flow Maps for Accelerated Samplingcited by 20
  35. 2025Terminal Velocity Matchingcited by 20
  36. 2026Diversity-Preserved Distribution Matching Distillation for Fast Visual Synthesiscited by 20
  37. 2024Mobile Video Diffusioncited by 18
  38. 2025CMT: Mid-Training for Efficient Learning of Consistency, Mean Flow, and Flow Map Modelscited by 18

50 most cited of 283 All 283 (JSON)

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  1. 2024Truncated Consistency Models
  2. 2024Towards Faster Training of Diffusion Models: An Inspiration of A Consistency Phenomenon
  3. 2024Stable Consistency Tuning: Understanding and Improving Consistency Models
  4. 2024Phased Consistency Models
  5. 2024Provable Statistical Rates for Consistency Diffusion Models
  6. 2024Towards a mathematical theory for consistency training in diffusion models
  7. 2025Beyond and Free from Diffusion: Invertible Guided Consistency Training
  8. 2025Image-Free Timestep Distillation via Continuous-Time Consistency with Trajectory-Sampled Pairs