mlsanityData to 7 Oct 2026

What does guidance do? A fine-grained analysis in a simple setting

arXiv 2409.13074 ↗First posted 19 Sep 2024cs.LG cs.CV stat.MLcited by 45

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

The use of guidance in diffusion models was originally motivated by the premise that the guidance-modified score is that of the data distribution tilted by a conditional likelihood raised to some power. In this work we clarify this misconception by rigorously proving that guidance fails to sample from the intended tilted distribution. Our main result is to give a fine-grained characterization of the dynamics of guidance in two cases, (1) mixtures of compactly supported distributions and (2) mixtures of Gaussians, which reflect salient properties of guidance that manifest on real-world data. In both cases, we prove that as the guidance parameter increases, the guided model samples more heavily from the boundary of the support of the conditional distribution. We also prove that for any nonzero level of score estimation error, sufficiently large guidance will result in sampling away from the support, theoretically justifying the empirical finding that large guidance results in distorted generations. In addition to verifying these results empirically in synthetic settings, we also show how our theoretical insights can offer useful prescriptions for practical deployment.

Key facts. Cited by 45 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 29 of its 35 references that are in the map. First posted on arXiv 19 Sep 2024.

Builds on

29 of 35 references.

Closest ancestors · 24

Same direction, newest first

  1. 2024Classifier-Free Guidance is a Predictor-Corrector16 Aug
  2. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models5 Aug
  3. 2024Guiding a Diffusion Model with a Bad Version of Itself4 Jun
  4. 2024Learning general Gaussian mixtures with efficient score matching29 Apr
  5. 2024Learning Mixtures of Gaussians Using Diffusion Models29 Apr
  6. 2024Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory18 Mar
  7. 2024Accelerating Convergence of Score-Based Diffusion Models, Provably6 Mar
  8. 2024Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian Mixture Models3 Mar
  9. 2024Critical windows: non-asymptotic theory for feature emergence in diffusion models3 Mar
  10. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  11. 2023Learning Mixtures of Gaussians Using the DDPM Objective3 Jul
  12. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models15 Jun
12 more
  1. 2023The probability flow ODE is provably fast19 May
  2. 2023Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC22 Feb
  3. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data14 Feb
  4. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  5. 2022Convergence of score-based generative modeling for general data distributions26 Sep
  6. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  7. 2022Classifier-Free Diffusion Guidance26 Jul
  8. 2021Score-based Generative Modeling in Latent Space10 Jun
  9. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  10. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  11. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  12. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 5

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  4. 2023Analysis of learning a flow-based generative model from limited sample complexitycited by 38
  5. 2024Diffusion Posterior Sampling is Computationally Intractablecited by 20

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 6; 2025: 22; 2026: 17.

45 papers.

Sort:

By area:

  1. 2025Low-dimensional adaptation of diffusion models: Convergence in total variationcited by 38
  2. 2024Stochastic Runge-Kutta Methods: Provable Acceleration of Diffusion Modelscited by 35
  3. 2025Debiasing Guidance for Discrete Diffusion with Sequential Monte Carlocited by 29
  4. 2025pi-Flow: Policy-Based Few-Step Generation via Imitation Distillationcited by 25
  5. 2025Dimension-Free Convergence of Diffusion Models for Approximate Gaussian Mixturescited by 23
  6. 2025DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Modelscited by 21
  7. 2024Rectified Diffusion Guidance for Conditional Generationcited by 18
  8. 2024How much is a noisy image worth? Data Scaling Laws for Ambient Diffusioncited by 18
  9. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  10. 2025A Closer Look at Model Collapse: From a Generalization-to-Memorization Perspectivecited by 18
  11. 2025Feedback Guidance of Diffusion Modelscited by 16
  12. 2025Stage-wise Dynamics of Classifier-Free Guidance in Diffusion Modelscited by 13
33 more
  1. 2025Learn to Guide Your Diffusion Modelcited by 12
  2. 2025Improving Classifier-Free Guidance in Masked Diffusion: Low-Dim Theoretical Insights with High-Dim Impactcited by 11
  3. 2025Adaptive Diffusion Guidance via Stochastic Optimal Controlcited by 9
  4. 2025What Exactly Does Guidance Do in Masked Discrete Diffusion Modelscited by 9
  5. 2025Provable Efficiency of Guidance in Diffusion Models for General Data Distributioncited by 8
  6. 2025Angle Domain Guidance: Latent Diffusion Requires Rotation Rather Than Extrapolationcited by 8
  7. 2025Composition and Alignment of Diffusion Models using Constrained Learningcited by 8
  8. 2025REG: Rectified Gradient Guidance for Conditional Diffusion Modelscited by 7
  9. 2024Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplerscited by 6
  10. 2025Towards a Golden Classifier-Free Guidance Path via Foresight Fixed Point Iterationscited by 6
  11. 2025AudioMoG: Guiding Audio Generation with Mixture-of-Guidancecited by 5
  12. 2026Steering diffusion models with quadratic rewards: a fine-grained analysiscited by 5
  13. 2025Conditional Diffusion Models with Classifier-Free Gibbs-like Guidancecited by 4
  14. 2026Emergence of Distortions in High-Dimensional Guided Diffusion Modelscited by 3
  15. 2024Feature-guided score diffusion for sampling conditional densitiescited by 2
  16. 2024A solvable generative model with a linear, one-step denoisercited by 2
  17. 2026Test-Time Conditioning with Representation-Aligned Visual Featurescited by 2
  18. 2026SURGE: Approximation and Training Free Particle Filter for Diffusion Surrogatecited by 2
  19. 2026Are we really tilting? The mechanics of reward guidance in flow and diffusion modelscited by 2
  20. 2025Studying Classifier(-Free) Guidance From a Classifier-Centric Perspectivecited by 1
  21. 2026When Are Two Scores Better Than One? Investigating Ensembles of Diffusion Modelscited by 1
  22. 2026Provably Reliable Classifier Guidance via Cross-Entropy Controlcited by 1
  23. 2026On the Robustness of Distribution Support under Diffusion Guidancecited by 1
  24. 2026The tractability landscape of diffusion alignment: regularization, rewards, and computational primitivescited by 1
  25. 2026FluxLite: Inference-Time Proposal Control for Discrete Diffusion Modelscited by 1
  26. 2025Disentangled representations via score-based variational autoencoderscited by 0
  27. 2026Learning To Sample From Diffusion Models Via Inverse Reinforcement Learningcited by 0
  28. 2026A Quantitative Approximation Framework for Flow Distillation in Diffusion Modelscited by 0
  29. 2026Information-Theoretic Classifier-Free Guidance with Adaptive Schedule Optimizationcited by 0
  30. 2026Not All Prediction Targets Keep Training-Free Diffusion Guidance on the Manifoldcited by 0
  31. 2026Guidance Breaks the Fitted Operator: A Terminal-Fitted Repair for Classifier-Free Guidancecited by 0
  32. 2026Adversarial Learning of Classifier-Free Guidance Schedulescited by 0
  33. 2026PathGuide: Dynamic Classifier-Free Guidance via On-Policy Transport Alignmentcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Applying Guidance in a Limited Interval Improves Sample and Distribution Quality in Diffusion Models
  2. 2023Bridging the Gap: Addressing Discrepancies in Diffusion Model Training for Classifier-Free Guidance
  3. 2025Towards a unified framework for guided diffusion models
  4. 2024Gradient Guidance for Diffusion Models: An Optimization Perspective
  5. 2025Stochastic Self-Guidance for Training-Free Enhancement of Diffusion Models
  6. 2026Analytic Distribution of Classifier-Free Guidance for Schedule Design
  7. 2026Visualizing Distribution Coverage in Generative Diffusion Models
  8. 2026C2FG: Control Classifier-Free Guidance via Score Discrepancy Analysis