mlsanityData to 7 Oct 2026

On the Equivalence of Consistency-Type Models: Consistency Models, Consistent Diffusion Models, and Fokker-Planck Regularization

arXiv 2306.00367 ↗First posted 1 Jun 2023cs.LG cs.AI math.STcited by 10

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

The emergence of various notions of ``consistency'' in diffusion models has garnered considerable attention and helped achieve improved sample quality, likelihood estimation, and accelerated sampling. Although similar concepts have been proposed in the literature, the precise relationships among them remain unclear. In this study, we establish theoretical connections between three recent ``consistency'' notions designed to enhance diffusion models for distinct objectives. Our insights offer the potential for a more comprehensive and encompassing framework for consistency-type models.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 15 of its 27 references that are in the map. First posted on arXiv 1 Jun 2023.

Builds on

15 of 27 references.

Closest ancestors · 7

Same direction, newest first

  1. 2023Consistency Models2 Mar
  2. 2023Consistent Diffusion Models: Mitigating Sampling Drift by Learning to be Consistent17 Feb
  3. 2022Refining Generative Process with Discriminator Guidance in Score-based Diffusion Models28 Nov
  4. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  5. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  6. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  7. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 8

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  4. 2022Denoising Diffusion Restoration Modelscited by 951
  5. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
  6. 2023GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restorationcited by 58
  7. 2022Probability flow solution of the Fokker-Planck equationcited by 46
  8. 2022Unsupervised vocal dereverberation with diffusion-based generative modelscited by 18

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 5; 2025: 1; 2026: 2.

10 papers.

  1. 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusioncited by 448
  2. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency modelscited by 99
  3. 2024Distillation of Discrete Diffusion through Dimensional Correlationscited by 46
  4. 2024Consistent Diffusion Meets Tweedie: Training Exact Ambient Diffusion Models with Noisy Datacited by 44
  5. 2023On Error Propagation of Diffusion Modelscited by 30
  6. 2025CMT: Mid-Training for Efficient Learning of Consistency, Mean Flow, and Flow Map Modelscited by 18
  7. 2024Improving Vector-Quantized Image Modeling with Latent Consistency-Matching Diffusioncited by 5
  8. 2024HERO: Human-Feedback Efficient Reinforcement Learning for Online Diffusion Model Finetuningcited by 4
  9. 2026On the Memorization of Consistency Distillation for Diffusion Modelscited by 0
  10. 2026Physics-Informed Generative Solver: Bridging Data-Driven Priors and Conservation Laws for Stable Spatiotemporal Field Reconstructioncited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Towards a mathematical theory for consistency training in diffusion models
  2. 2025Multi-Step Consistency Models: Fast Generation with Theoretical Guarantees
  3. 2024Provable Statistical Rates for Consistency Diffusion Models
  4. 2023The Emergence of Reproducibility and Generalizability in Diffusion Models
  5. 2026Consistent Diffusion Language Models
  6. 2025Convergence Of Consistency Model With Multistep Sampling Under General Data Assumptions
  7. 2024Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models
  8. 2026A Mathematical Introduction to Diffusion Models