mlsanityData to 7 Oct 2026

An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization

arXiv 2404.07771 ↗First posted 11 Apr 2024cs.LG math.ST stat.MLcited by 72

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible high-dimensional data modeling, and act as a sampler for generating new samples under active guidance towards task-desired properties. Despite the significant empirical success, theory of diffusion models is very limited, potentially slowing down principled methodological innovations for further harnessing and improving diffusion models. In this paper, we review emerging applications of diffusion models, understanding their sample generation under various controls. Next, we overview the existing theories of diffusion models, covering their statistical properties and sampling capabilities. We adopt a progressive routine, beginning with unconditional diffusion models and connecting to conditional counterparts. Further, we review a new avenue in high-dimensional structured optimization through conditional diffusion models, where searching for solutions is reformulated as a conditional sampling problem and solved by diffusion models. Lastly, we discuss future directions about diffusion models. The purpose of this paper is to provide a well-rounded theoretical exposure for stimulating forward-looking theories and methods of diffusion models.

Key facts. Cited by 72 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 167 of its 211 references that are in the map. First posted on arXiv 11 Apr 2024.

Builds on

167 of 211 references.

Closest ancestors · 58

Same direction, newest first

  1. 2024Diffusion Model for Data-Driven Black-Box Optimization20 Mar
  2. 2024Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory18 Mar
  3. 2024Fine-tuning of diffusion models via stochastic control: entropy regularization and beyond10 Mar
  4. 2024Accelerating Convergence of Score-Based Diffusion Models, Provably6 Mar
  5. 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesis5 Mar
  6. 2024Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian Mixture Models3 Mar
  7. 2024Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformization12 Feb
  8. 2024Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorial12 Feb
  9. 2024Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalization28 Jan
  10. 2023LCM-LoRA: A Universal Stable-Diffusion Acceleration Module9 Nov
  11. 2023State of the Art on Diffusion Models for Visual Computing11 Oct
  12. 2023Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Models20 Sep
38 more
  1. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  2. 2023Learning Mixtures of Gaussians Using the DDPM Objective3 Jul
  3. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models15 Jun
  4. 2023Diffusion Models for Black-Box Optimization12 Jun
  5. 2023The probability flow ODE is provably fast19 May
  6. 2023Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces18 May
  7. 2023Reflected Diffusion Models10 Apr
  8. 2023End-to-End Diffusion Latent Optimization Improves Classifier Guidance23 Mar
  9. 2023Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers6 Mar
  10. 2023Diffusion Models are Minimax Optimal Distribution Estimators3 Mar
  11. 2023Consistency Models2 Mar
  12. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data14 Feb
  13. 2023Universal Guidance for Diffusion Models14 Feb
  14. 2022Scalable Diffusion Models with Transformers19 Dec
  15. 2022Score-based Continuous-time Discrete Diffusion Models30 Nov
  16. 2022From Denoising Diffusions to Denoising Markov Models7 Nov
  17. 2022Efficient Diffusion Models for Vision: A Survey7 Oct
  18. 2022Convergence of score-based generative modeling for general data distributions26 Sep
  19. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  20. 2022Diffusion Models in Vision: A Survey10 Sep
  21. 2022Diffusion Models: A Comprehensive Survey of Methods and Applications2 Sep
  22. 2022Let us Build Bridges: Understanding and Extending Diffusion Generative Models31 Aug
  23. 2022Understanding Diffusion Models: A Unified Perspective25 Aug
  24. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  25. 2022Classifier-Free Diffusion Guidance26 Jul
  26. 2022Convergence for score-based generative modeling with polynomial complexity13 Jun
  27. 2022gDDIM: Generalized denoising diffusion implicit models11 Jun
  28. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  29. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  30. 2022A Continuous Time Framework for Discrete Denoising Models30 May
  31. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  32. 2022Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality11 Feb
  33. 2022Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models17 Jan
  34. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  35. 2021Vector Quantized Diffusion Model for Text-to-Image Synthesis29 Nov
  36. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models6 Aug
  37. 2021Structured Denoising Diffusion Models in Discrete State-Spaces7 Jul
  38. 2021Score-based Generative Modeling in Latent Space10 Jun

50 newest of 58 All 58 (JSON)

Other references · 109

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  3. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  4. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  5. 2022Generative Adversarial Networkscited by 5,603
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  7. 2021On the Opportunities and Risks of Foundation Modelscited by 3,961
  8. 2023Diffusion Policy: Visuomotor Policy Learning via Action Diffusioncited by 2,730
  9. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,609
  10. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  11. 2021Decision Transformer: Reinforcement Learning via Sequence Modelingcited by 1,528
  12. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
38 more
  1. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,419
  2. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  3. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  4. 2021Palette: Image-to-Image Diffusion Modelscited by 1,296
  5. 2022Human Motion Diffusion Modelcited by 1,062
  6. 2022Planning with Diffusion for Flexible Behavior Synthesiscited by 1,023
  7. 2023ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generationcited by 1,010
  8. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,006
  9. 2019An Introduction to Variational Autoencoderscited by 997
  10. 2022Denoising Diffusion Restoration Modelscited by 951
  11. 2023Training Diffusion Models with Reinforcement Learningcited by 939
  12. 2021Blended Diffusion for Text-driven Editing of Natural Imagescited by 924
  13. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  14. 2019Plug and Play Language Models: A Simple Approach to Controlled Text Generationcited by 793
  15. 2021DiffusionCLIP: Text-Guided Diffusion Models for Robust Image Manipulationcited by 640
  16. 2021Offline Reinforcement Learning as One Big Sequence Modeling Problemcited by 636
  17. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 620
  18. 2017Generative Adversarial Networks: An Overviewcited by 588
  19. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 577
  20. 2022Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Modelcited by 574
  21. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
  22. 2022Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learningcited by 543
  23. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  24. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
  25. 2022Is Conditional Generative Modeling all you need for Decision-Making?cited by 504
  26. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 501
  27. 2022Diffusion Models for Adversarial Purificationcited by 469
  28. 2024Sora: A Review on Background, Technology, Limitations, and Opportunities of Large Vision Modelscited by 467
  29. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 431
  30. 2023DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Modelscited by 431
  31. 2023Directly Fine-Tuning Diffusion Models on Differentiable Rewardscited by 431
  32. 2023Aligning Text-to-Image Models using Human Feedbackcited by 418
  33. 2021SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Modelscited by 415
  34. 2023InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generationcited by 387
  35. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
  36. 2020Is Pessimism Provably Efficient for Offline RL?cited by 362
  37. 2021Score-based diffusion models for accelerated MRIcited by 308
  38. 2023IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policiescited by 307

50 most cited of 109 All 109 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 24; 2025: 28; 2026: 20.

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  1. 2025MMaDA: Multimodal Large Diffusion Language Modelscited by 241
  2. 2024Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Reviewcited by 92
  3. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Modelscited by 64
  4. 2024Gradient Guidance for Diffusion Models: An Optimization Perspectivecited by 59
  5. 2024How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Frameworkcited by 48
  6. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexitycited by 42
  7. 2024On Statistical Rates and Provably Efficient Criteria of Latent Diffusion Transformers (DiTs)cited by 39
  8. 2025Hydra-NeXt: Robust Closed-Loop Driving with Open-Loop Trainingcited by 39
  9. 2025Low-dimensional adaptation of diffusion models: Convergence in total variationcited by 38
  10. 2024Stochastic Runge-Kutta Methods: Provable Acceleration of Diffusion Modelscited by 35
  11. 2025Efficient Diffusion Models: A Surveycited by 35
  12. 2024From optimal score matching to optimal samplingcited by 27
38 more
  1. 2024Provable Acceleration for Diffusion Models under Minimal Assumptionscited by 27
  2. 2024Evaluating the design space of diffusion-based generative modelscited by 25
  3. 2024Preference Tuning with Human Feedback on Language, Speech, and Vision Tasks: A Surveycited by 23
  4. 2025Minimax Optimality of the Probability Flow ODE for Diffusion Modelscited by 23
  5. 2024On Statistical Rates of Conditional Diffusion Transformers: Approximation, Estimation and Minimax Optimalitycited by 21
  6. 2024Constrained Diffusion Models via Dual Trainingcited by 19
  7. 2024Reward-Directed Score-Based Diffusion Models via q-Learningcited by 18
  8. 2024U-Nets as Belief Propagation: Efficient Classification, Denoising, and Diffusion in Generative Hierarchical Modelscited by 17
  9. 2024Diffusion-Based Visual Art Creation: A Survey and New Perspectivescited by 17
  10. 2025Advancing Wasserstein Convergence Analysis of Score-Based Models: Insights from Discretization and Second-Order Accelerationcited by 17
  11. 2025Your Vision-Language Model Can't Even Count to 20: Exposing the Failures of VLMs in Compositional Countingcited by 17
  12. 2025Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradientscited by 15
  13. 2026Conditional Diffusion Guidance under Hard Constraint: A Stochastic Analysis Approachcited by 10
  14. 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Boundscited by 8
  15. 2026The data geometry of masking diffusion: Certified-optimal schedules via unmasking growth complexitycited by 8
  16. 2025Fast Direct: Query-Efficient Online Black-box Guidance for Diffusion-model Target Generationcited by 7
  17. 2026High-accuracy and dimension-free sampling with diffusionscited by 7
  18. 2024Diffusion Transformer Captures Spatial-Temporal Dependencies: A Theory for Gaussian Process Datacited by 5
  19. 2025Localized Diffusion Modelscited by 5
  20. 2026Do Less, Achieve More: Do We Need Every-Step Optimization for RL Fine-tuning of Diffusion Models?cited by 5
  21. 2024Deep Generative Classification of Blood Cell Morphologycited by 4
  22. 2025Evaluating and Predicting Distorted Human Body Parts for Generated Imagescited by 4
  23. 2025Evolvable Conditional Diffusioncited by 4
  24. 2025Fast Score-Based Sampling via Log-Concave Reductionscited by 4
  25. 2024Model Free Prediction with Uncertainty Assessmentcited by 3
  26. 2025Superscopes: Amplifying Internal Feature Representations for Language Model Interpretationcited by 3
  27. 2024Differentially Private Kernel Density Estimationcited by 2
  28. 2024Channel-aware Contrastive Conditional Diffusion for Multivariate Probabilistic Time Series Forecastingcited by 2
  29. 2025Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Accesscited by 2
  30. 2025Discovering Latent Graphs with GFlowNets for Diverse Conditional Image Generationcited by 2
  31. 2026Denoising growth complexity: Data geometry and certified schedules for diffusion samplingcited by 2
  32. 2026The information geometry of product-reference discrete diffusion: Interaction growth complexity and optimal schedulingcited by 2
  33. 2024New algorithms for sampling and diffusion modelscited by 1
  34. 2025MAP-based Problem-Agnostic diffusion model for Inverse Problemscited by 1
  35. 2025Belief-Conditioned One-Step Diffusion: Real-Time Trajectory Planning with Just-Enough Sensingcited by 1
  36. 2025Non-Identical Diffusion Models in MIMO-OFDM Channel Generationcited by 1
  37. 2025SurvDiff: A Diffusion Model for Generating Synthetic Data in Survival Analysiscited by 1
  38. 2025CINDES: Classification induced neural density estimator and simulatorcited by 1

50 most cited of 72 All 72 (JSON)

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