mlsanityData to 14 Oct 2026

Towards a unified framework for guided diffusion models

arXiv 2512.04985 ↗First posted 4 Dec 2025stat.ML cs.LG math.STcited by 8

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Guided or controlled data generation with diffusion modelsblfootnotePartial preliminary results of this work appeared in International Conference on Machine Learning 2025 citepli2025provable. has become a cornerstone of modern generative modeling. Despite substantial advances in diffusion model theory, the theoretical understanding of guided diffusion samplers remains severely limited. We make progress by developing a unified algorithmic and theoretical framework that accommodates both diffusion guidance and reward-guided diffusion. Aimed at fine-tuning diffusion models to improve certain rewards, we propose injecting a reward guidance term -- constructed from the difference between the original and reward-reweighted scores -- into the backward diffusion process, and rigorously quantify the resulting reward improvement over the unguided counterpart. As a key application, our framework shows that classifier-free guidance (CFG) decreases the expected reciprocal of the classifier probability, providing the first theoretical characterization of the specific performance metric that CFG improves for general target distributions. When applied to reward-guided diffusion, our framework yields a new sampler that is easy-to-train and requires no full diffusion trajectories during training. Numerical experiments further corroborate our theoretical findings.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 43 of its 77 references that are in the map. First posted on arXiv 4 Dec 2025.

Builds on

43 of 77 references.

Closest ancestors · 29

Same direction, newest first

  1. 2025Sublinear iterations can suffice even for DDPMs6 Nov
  2. 2025Optimal Convergence Analysis of DDPM for General Distributions31 Oct
  3. 2025The Principles of Diffusion Models24 Oct
  4. 2025Learn to Guide Your Diffusion Model1 Oct
  5. 2025Stage-wise Dynamics of Classifier-Free Guidance in Diffusion Models26 Sep
  6. 2025Improving Classifier-Free Guidance in Masked Diffusion: Low-Dim Theoretical Insights with High-Dim Impact11 Jul
  7. 2025Faster Diffusion Models via Higher-Order Approximation30 Jun
  8. 2025What Exactly Does Guidance Do in Masked Discrete Diffusion Models12 Jun
  9. 2025Towards Understanding the Mechanisms of Classifier-Free Guidance25 May
  10. 2025Provable Efficiency of Guidance in Diffusion Models for General Data Distribution2 May
  11. 2025Dimension-Free Convergence of Diffusion Models for Approximate Gaussian Mixtures7 Apr
  12. 2025Minimax Optimality of the Probability Flow ODE for Diffusion Models12 Mar
17 more
  1. 2025Low-dimensional adaptation of diffusion models: Convergence in total variation22 Jan
  2. 2024Simple Guidance Mechanisms for Discrete Diffusion Models13 Dec
  3. 2024Provable Acceleration for Diffusion Models under Minimal Assumptions30 Oct
  4. 2024Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality24 Oct
  5. 2024Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers17 Oct
  6. 2024Instance-dependent Convergence Theory for Diffusion Models17 Oct
  7. 2024Linear Convergence of Diffusion Models Under the Manifold Hypothesis11 Oct
  8. 2024Stochastic Runge-Kutta Methods: Provable Acceleration of Diffusion Models7 Oct
  9. 2024Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions27 Sep
  10. 2024Classifier-Free Guidance is a Predictor-Corrector16 Aug
  11. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models5 Aug
  12. 2024Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallel3 Jun
  13. 2024Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models23 May
  14. 2024Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory18 Mar
  15. 2024Theoretical Insights for Diffusion Guidance: A Case Study for Gaussian Mixture Models3 Mar
  16. 2024Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorial12 Feb
  17. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep

Other references · 14

  1. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  2. 2019Fine-Tuning Language Models from Human Preferencescited by 2,150
  3. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,416
  4. 2023Training Diffusion Models with Reinforcement Learningcited by 982
  5. 2023Directly Fine-Tuning Diffusion Models on Differentiable Rewardscited by 448
  6. 2024Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Controlcited by 143
  7. 2024Unlocking Guidance for Discrete State-Space Diffusion and Flow Modelscited by 129
  8. 2024Understanding Reinforcement Learning-Based Fine-Tuning of Diffusion Models: A Tutorial and Reviewcited by 98
  9. 2024Reward-Directed Score-Based Diffusion Models via q-Learningcited by 19
  10. 2024Scores as Actions: a framework of fine-tuning diffusion models by continuous-time reinforcement learningcited by 19
  11. 2025Classifier-Free Guidance: From High-Dimensional Analysis to Generalized Guidance Formscited by 10
  12. 2025Maximize Your Diffusion: A Study into Reward Maximization and Alignment for Diffusion-based Controlcited by 2
2 more
  1. 2025A Reward-Directed Diffusion Framework for Generative Design Optimizationcited by 2
  2. 2025Connections between reinforcement learning with feedback,test-time scaling, and diffusion guidance: An anthologycited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 8.

8 papers.

  1. 2026Inference-Time Alignment for Diffusion Models via Variationally Stable Doob's Matchingcited by 5
  2. 2026Emergence of Distortions in High-Dimensional Guided Diffusion Modelscited by 4
  3. 2026Provably Reliable Classifier Guidance via Cross-Entropy Controlcited by 1
  4. 2026On the Robustness of Distribution Support under Diffusion Guidancecited by 1
  5. 2026Slowly Annealed Langevin Dynamics: Theory and Applications to Training-Free Guided Generationcited by 1
  6. 2026CausalGDP: Causality-Guided Diffusion Policies for Reinforcement Learningcited by 0
  7. 2026Particle Dynamics of Flow Matching and Classifier-Free Guidance from a Stagewise Geometry Perspectivecited by 0
  8. 2026Steepest Guidance: A Practical and Principled Approach to Inference-Time Alignment of Flow and Diffusion-based Modelscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Bridging the Gap: Addressing Discrepancies in Diffusion Model Training for Classifier-Free Guidance
  2. 2024Gradient Guidance for Diffusion Models: An Optimization Perspective
  3. 2023Towards Controllable Diffusion Models via Reward-Guided Exploration
  4. 2024TFG: Unified Training-Free Guidance for Diffusion Models
  5. 2023Elucidating The Design Space of Classifier-Guided Diffusion Generation
  6. 2024Rectified Diffusion Guidance for Conditional Generation
  7. 2025Stochastic Self-Guidance for Training-Free Enhancement of Diffusion Models
  8. 2025Feedback Guidance of Diffusion Models