mlsanityData to 7 Oct 2026

Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory

arXiv 2403.11968 ↗First posted 18 Mar 2024cs.LG math.ST stat.MLcited by 58

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate various conditional information, such as prompt input, to guide the sample generation towards desired properties. Despite the empirical success, theory of conditional diffusion models is largely missing. This paper bridges this gap by presenting a sharp statistical theory of distribution estimation using conditional diffusion models. Our analysis yields a sample complexity bound that adapts to the smoothness of the data distribution and matches the minimax lower bound. The key to our theoretical development lies in an approximation result for the conditional score function, which relies on a novel diffused Taylor approximation technique. Moreover, we demonstrate the utility of our statistical theory in elucidating the performance of conditional diffusion models across diverse applications, including model-based transition kernel estimation in reinforcement learning, solving inverse problems, and reward conditioned sample generation.

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 48 of its 99 references that are in the map. First posted on arXiv 18 Mar 2024.

Builds on

48 of 99 references.

Closest ancestors · 14

Same direction, newest first

  1. 2023Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Models20 Sep
  2. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  3. 2023Learning Mixtures of Gaussians Using the DDPM Objective3 Jul
  4. 2023The probability flow ODE is provably fast19 May
  5. 2023Diffusion Models are Minimax Optimal Distribution Estimators3 Mar
  6. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data14 Feb
  7. 2022Efficient Diffusion Models for Vision: A Survey7 Oct
  8. 2022Convergence of score-based generative modeling for general data distributions26 Sep
  9. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  10. 2022Let us Build Bridges: Understanding and Extending Diffusion Generative Models31 Aug
  11. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  12. 2022Classifier-Free Diffusion Guidance26 Jul
2 more
  1. 2022Convergence for score-based generative modeling with polynomial complexity13 Jun
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov

Other references · 34

  1. 2023Diffusion Policy: Visuomotor Policy Learning via Action Diffusioncited by 2,730
  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. 2022Human Motion Diffusion Modelcited by 1,062
  5. 2022Planning with Diffusion for Flexible Behavior Synthesiscited by 1,023
  6. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  7. 2019Plug and Play Language Models: A Simple Approach to Controlled Text Generationcited by 793
  8. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 620
  9. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  10. 2022GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generationcited by 511
  11. 2022Is Conditional Generative Modeling all you need for Decision-Making?cited by 504
  12. 2023IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policiescited by 307
22 more
  1. 2023Imitating Human Behaviour with Diffusion Modelscited by 260
  2. 2023Goal-Conditioned Imitation Learning using Score-based Diffusion Policiescited by 229
  3. 2022Structure-based Drug Design with Equivariant Diffusion Modelscited by 213
  4. 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 195
  5. 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistencycited by 180
  6. 2021Diff-TTS: A Denoising Diffusion Model for Text-to-Speechcited by 156
  7. 2023Protein Design with Guided Discrete Diffusioncited by 154
  8. 2021Symbolic Music Generation with Diffusion Modelscited by 152
  9. 2020Generative Modeling with Denoising Auto-Encoders and Langevin Samplingcited by 118
  10. 2023Diffusion Models for Image Restoration and Enhancement: A Comprehensive Surveycited by 108
  11. 2022Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Modelscited by 97
  12. 2024Optimal score estimation via empirical Bayes smoothingcited by 60
  13. 2023Reward-Directed Conditional Diffusion: Provable Distribution Estimation and Reward Improvementcited by 49
  14. 2023Graph Denoising Diffusion for Inverse Protein Foldingcited by 44
  15. 2022High-Frequency Space Diffusion Models for Accelerated MRIcited by 41
  16. 2023Sampling, Diffusions, and Stochastic Localizationcited by 38
  17. 20223DLinker: An E(3) Equivariant Variational Autoencoder for Molecular Linker Designcited by 33
  18. 2022A Diffusion Model Predicts 3D Shapes from 2D Microscopy Imagescited by 24
  19. 2023Reliable Generation of Privacy-preserving Synthetic Electronic Health Record Time Series via Diffusion Modelscited by 24
  20. 2022Metal Inpainting in CBCT Projections Using Score-based Generative Modelcited by 7
  21. 2023Efficient Reinforcement Learning with Impaired Observability: Learning to Act with Delayed and Missing State Observationscited by 4
  22. 2023Actions Speak What You Want: Provably Sample-Efficient Reinforcement Learning of the Quantal Stackelberg Equilibrium from Strategic Feedbackscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 16; 2025: 24; 2026: 18.

58 papers.

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  1. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimizationcited by 72
  2. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Modelscited by 64
  3. 2024Gradient Guidance for Diffusion Models: An Optimization Perspectivecited by 59
  4. 2024What does guidance do? A fine-grained analysis in a simple settingcited by 45
  5. 2025Low-dimensional adaptation of diffusion models: Convergence in total variationcited by 38
  6. 2024On Statistical Rates of Conditional Diffusion Transformers: Approximation, Estimation and Minimax Optimalitycited by 21
  7. 2024U-Nets as Belief Propagation: Efficient Classification, Denoising, and Diffusion in Generative Hierarchical Modelscited by 17
  8. 2025Provable Separations between Memorization and Generalization in Diffusion Modelscited by 14
  9. 2025A Theoretical Analysis of Discrete Flow Matching Generative Modelscited by 13
  10. 2025Learn to Guide Your Diffusion Modelcited by 12
  11. 2024Conditional Diffusion Models Based Conditional Independence Testingcited by 9
  12. 2025Towards a unified framework for guided diffusion modelscited by 7
38 more
  1. 2024Enhancing Accuracy in Generative Models via Knowledge Transfercited by 6
  2. 2024Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplerscited by 6
  3. 2025Towards a Golden Classifier-Free Guidance Path via Foresight Fixed Point Iterationscited by 6
  4. 2024Diffusion Transformer Captures Spatial-Temporal Dependencies: A Theory for Gaussian Process Datacited by 5
  5. 2025Provable Sample-Efficient Transfer Learning Conditional Diffusion Models via Representation Learningcited by 5
  6. 2025Dynamic data generation and dynamic portfolio selection: an application of a score-based diffusion modelcited by 5
  7. 2025On Flow Matching KL Divergencecited by 5
  8. 2025Diffusion on Graph: Augmentation of Graph Structure for Node Classificationcited by 4
  9. 2024Model Free Prediction with Uncertainty Assessmentcited by 3
  10. 2025Can Diffusion Models Disentangle? A Theoretical Perspectivecited by 3
  11. 2026Emergence of Distortions in High-Dimensional Guided Diffusion Modelscited by 3
  12. 2024Differentially Private Kernel Density Estimationcited by 2
  13. 2024Automatic Scene Generation: State-of-the-Art Techniques, Models, Datasets, Challenges, and Future Prospectscited by 2
  14. 2025Diffusion Models with Double Guidance: Generate with aggregated datasetscited by 2
  15. 2025Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Accesscited by 2
  16. 2025Autoregressive regularized score-based diffusion models for multi-scenarios fluid flow predictioncited by 2
  17. 2025Expert-Guided Diffusion Planner for Auto-Biddingcited by 2
  18. 2025Schr"odinger bridge for generative AI: Soft-constrained formulation and convergence analysiscited by 2
  19. 2026Inference-Time Alignment for Diffusion Models via Variationally Stable Doob's Matchingcited by 2
  20. 2024Efficient Fine-Grained Guidance for Diffusion Model Based Symbolic Music Generationcited by 1
  21. 2024Semi-Implicit Functional Gradient Flow for Efficient Samplingcited by 1
  22. 2025A Theory for Conditional Generative Modeling on Multiple Data Sourcescited by 1
  23. 2025Non-asymptotic convergence bound of conditional diffusion modelscited by 1
  24. 2025Generating solution paths of Markovian stochastic differential equations using diffusion modelscited by 1
  25. 2026Multi-Subspace Multi-Modal Modeling for Diffusion Models: Estimation, Convergence and Mixture of Expertscited by 1
  26. 2026Diffusion Models for Adaptive Sequential Data Generationcited by 1
  27. 2024RCDM: Enabling Robustness for Conditional Diffusion Modelcited by 0
  28. 2025Conditionally Whitened Generative Models for Probabilistic Time Series Forecastingcited by 0
  29. 2025Factor-Based Conditional Diffusion Model for Contextual Portfolio Optimizationcited by 0
  30. 2025Diffusion Transformers for Imputation: Statistical Efficiency and Uncertainty Quantificationcited by 0
  31. 2025FoilDiff: A Hybrid Transformer Backbone for Diffusion-based Modelling of 2D Airfoil Flow Fieldscited by 0
  32. 2025Learning Causal States Under Partial Observability and Perturbationcited by 0
  33. 2026Generative and Nonparametric Approaches for Conditional Distribution Estimation: Methods, Perspectives, and Comparative Evaluationscited by 0
  34. 2026LLM-Inspired Pretrain-Then-Finetune for Small-Data, Large-Scale Optimizationcited by 0
  35. 2026DP-aware AdaLN-Zero: Taming Conditioning-Induced Heavy-Tailed Gradients in Differentially Private Diffusioncited by 0
  36. 2026Tucker Diffusion Model for High-dimensional Tensor Generationcited by 0
  37. 2026Universality of Gaussian-Mixture Reverse Kernels in Conditional Diffusioncited by 0
  38. 2026Causality-Encoded Diffusion Models for Interventional Sampling and Edge Inferencecited by 0

50 most cited of 58 All 58 (JSON)

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  1. 2023CADS: Unleashing the Diversity of Diffusion Models through Condition-Annealed Sampling
  2. 2025Capturing Conditional Dependence via Auto-regressive Diffusion Models
  3. 2024Conditional sampling within generative diffusion models
  4. 2021Conditional Image Generation with Score-Based Diffusion Models
  5. 2026A Plug-in Interpretation of Conditioning in Score-Based Diffusion Models
  6. 2025REG: Rectified Gradient Guidance for Conditional Diffusion Models
  7. 2023Towards Controllable Diffusion Models via Reward-Guided Exploration
  8. 2024Improving Training-free Conditional Diffusion Model via Fisher Information