mlsanityData to 7 Oct 2026

From Denoising Diffusions to Denoising Markov Models

arXiv 2211.03595 ↗First posted 7 Nov 2022stat.ML cs.LGcited by 58

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Denoising diffusions are state-of-the-art generative models exhibiting remarkable empirical performance. They work by diffusing the data distribution into a Gaussian distribution and then learning to reverse this noising process to obtain synthetic datapoints. The denoising diffusion relies on approximations of the logarithmic derivatives of the noised data densities using score matching. Such models can also be used to perform approximate posterior simulation when one can only sample from the prior and likelihood. We propose a unifying framework generalising this approach to a wide class of spaces and leading to an original extension of score matching. We illustrate the resulting models on various applications.

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 16 of its 35 references that are in the map. First posted on arXiv 7 Nov 2022.

Builds on

16 of 35 references.

Closest ancestors · 6

Same direction, newest first

  1. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  2. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  3. 2022A Continuous Time Framework for Discrete Denoising Models30 May
  4. 2022Riemannian Score-Based Generative Modelling6 Feb
  5. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  6. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 10

  1. 2020Language Models are Few-Shot Learnerscited by 32,199
  2. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,441
  3. 2019Neural Spline Flowscited by 590
  4. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
  5. 2018Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flowscited by 217
  6. 2019Automatic Posterior Transformation for Likelihood-Free Inferencecited by 216
  7. 2020On Contrastive Learning for Likelihood-free Inferencecited by 96
  8. 2019Approximate Bayesian computation with the Wasserstein distancecited by 34
  9. 2020A new method for parameter estimation in probabilistic models: Minimum probability flowcited by 5
  10. 2015Exact simulation of the Wright-Fisher diffusioncited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 7; 2024: 17; 2025: 19; 2026: 15.

58 papers.

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  1. 2024Simple and Effective Masked Diffusion Language Modelscited by 800
  2. 2024Simplified and Generalized Masked Diffusion for Discrete Datacited by 606
  3. 2024Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Reviewcited by 92
  4. 2025Path Planning for Masked Diffusion Model Samplingcited by 79
  5. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimizationcited by 72
  6. 2023Monte Carlo guided Diffusion for Bayesian linear inverse problemscited by 65
  7. 2023Particle Guidance: non-I.I.D. Diverse Sampling with Diffusion Modelscited by 65
  8. 2023Towards Coherent Image Inpainting Using Denoising Diffusion Implicit Modelscited by 61
  9. 2024Informed Correctors for Discrete Diffusion Modelscited by 57
  10. 2024Discrete Copula Diffusioncited by 53
  11. 2024How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Frameworkcited by 48
  12. 2025Any-Order Flexible Length Masked Diffusioncited by 48
38 more
  1. 2025Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithmscited by 47
  2. 2024Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformizationcited by 44
  3. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
  4. 2025Fine-Tuning Discrete Diffusion Models with Policy Gradient Methodscited by 36
  5. 2023Trans-Dimensional Generative Modeling via Jump Diffusion Modelscited by 33
  6. 2025Improving Reasoning for Diffusion Language Models via Group Diffusion Policy Optimizationcited by 30
  7. 2024Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysiscited by 24
  8. 2025MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Controlcited by 20
  9. 2025Diffuse Everything: Multimodal Diffusion Models on Arbitrary State Spacescited by 19
  10. 2024Conditional sampling within generative diffusion modelscited by 18
  11. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  12. 2026Rethinking the Design Space of Reinforcement Learning for Diffusion Models: On the Importance of Likelihood Estimation Beyond Loss Designcited by 17
  13. 2023Renormalizing Diffusion Modelscited by 16
  14. 2024Promises, Outlooks and Challenges of Diffusion Language Modelingcited by 11
  15. 2023Unbalanced Diffusion Schr"odinger Bridgecited by 9
  16. 2025Error Analysis of Discrete Flow with Generator Matchingcited by 9
  17. 2026Discrete Feynman-Kac Correctorscited by 9
  18. 2024Statistical guarantees for denoising reflected diffusion modelscited by 6
  19. 2025Almost Linear Convergence under Minimal Score Assumptions: Quantized Transition Diffusioncited by 6
  20. 2025Discrete Guidance Matching: Exact Guidance for Discrete Flow Matchingcited by 6
  21. 2024Diffusion Transformer Captures Spatial-Temporal Dependencies: A Theory for Gaussian Process Datacited by 5
  22. 2025Generative modelling with jump-diffusionscited by 4
  23. 2025Generative diffusion posterior sampling for informative likelihoodscited by 4
  24. 2025Algorithm- and Data-Dependent Generalization Bounds for Diffusion Modelscited by 4
  25. 2024Model Free Prediction with Uncertainty Assessmentcited by 3
  26. 2024Data Augmentation for Multivariate Time Series Classification: An Experimental Studycited by 3
  27. 2025Dimension-free error estimate for diffusion model and optimal schedulingcited by 3
  28. 2026Count Bridges enable Modeling and Deconvolving Transcriptomic Datacited by 3
  29. 2023Bayesian ECG reconstruction using denoising diffusion generative modelscited by 2
  30. 2025A Jump-Diffusion Framework for Irregular Time Series Generationcited by 2
  31. 2026CountsDiff: A Diffusion Model on the Natural Numbers for Generation and Imputation of Count-Based Datacited by 2
  32. 2026The information geometry of product-reference discrete diffusion: Interaction growth complexity and optimal schedulingcited by 2
  33. 2025Foundations of Diffusion Models in General State Spaces: A Self-Contained Introductioncited by 1
  34. 2025A Unification of Discrete, Gaussian, and Simplicial Diffusioncited by 1
  35. 2026Drift Estimation for Stochastic Differential Equations with Denoising Diffusion Modelscited by 1
  36. 2026Learning Discrete Diffusion of Graphs via Free-Energy Gradient Flowscited by 1
  37. 2026A Continuous-Time Reinforcement Learning Framework for Fine-Tuning Discrete Diffusion Modelscited by 1
  38. 2026Mean-to-Score Discrete Diffusion: Posterior-Mean Denoisers for Score Entropycited by 1

50 most cited of 58 All 58 (JSON)

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  1. 2023Denoising Diffusion Samplers
  2. 2023To smooth a cloud or to pin it down: Guarantees and Insights on Score Matching in Denoising Diffusion Models
  3. 2024Discrete vs. Continuous Trade-offs for Generative Models
  4. 2024Particle Denoising Diffusion Sampler
  5. 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
  6. 2024What's the score? Automated Denoising Score Matching for Nonlinear Diffusions
  7. 2025Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curves
  8. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions