mlsanityData to 14 Oct 2026

Faster Diffusion Models via Higher-Order Approximation

arXiv 2506.24042 ↗First posted 30 Jun 2025cs.LG cs.NA math.NAcited by 16

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

In this paper, we explore provable acceleration of diffusion models without any additional retraining. Focusing on the task of approximating a target data distribution in ℝd to within varepsilon total-variation distance, we propose a principled, training-free sampling algorithm that requires only the order of d1+2/K varepsilon-1/K score function evaluations (up to log factor) in the presence of accurate scores, where K>0 is an arbitrary fixed integer. This result applies to a broad class of target data distributions, without the need for assumptions such as smoothness or log-concavity. Our theory is robust vis-a-vis inexact score estimation, degrading gracefully as the score estimation error increases -- without demanding higher-order smoothness on the score estimates as assumed in previous work. The proposed algorithm draws insight from high-order ODE solvers, leveraging high-order Lagrange interpolation and successive refinement to approximate the integral derived from the probability flow ODE. More broadly, our work develops a theoretical framework towards understanding the efficacy of high-order methods for accelerated sampling.

Key facts. Cited by 16 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 49 of its 55 references that are in the map. First posted on arXiv 30 Jun 2025.

Builds on

49 of 55 references.

Closest ancestors · 46

Same direction, newest first

  1. 2025Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models16 Jun
  2. 2025Dimension-Free Convergence of Diffusion Models for Approximate Gaussian Mixtures7 Apr
  3. 2025Minimax Optimality of the Probability Flow ODE for Diffusion Models12 Mar
  4. 2025Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Models31 Jan
  5. 2025Low-dimensional adaptation of diffusion models: Convergence in total variation22 Jan
  6. 2024Provable Acceleration for Diffusion Models under Minimal Assumptions30 Oct
  7. 2024Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality24 Oct
  8. 2024Unified Convergence Analysis for Score-Based Diffusion Models with Deterministic Samplers18 Oct
  9. 2024Instance-dependent Convergence Theory for Diffusion Models17 Oct
  10. 2024Linear Convergence of Diffusion Models Under the Manifold Hypothesis11 Oct
  11. 2024Stochastic Runge-Kutta Methods: Provable Acceleration of Diffusion Models7 Oct
  12. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions27 Sep
34 more
  1. 2024Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions27 Sep
  2. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models5 Aug
  3. 2024Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models23 May
  4. 2024Convergence Analysis of Probability Flow ODE for Score-based Generative Models15 Apr
  5. 2024Accelerating Convergence of Score-Based Diffusion Models, Provably6 Mar
  6. 2024Broadening Target Distributions for Accelerated Diffusion Models via a Novel Analysis Approach21 Feb
  7. 2024Towards a mathematical theory for consistency training in diffusion models12 Feb
  8. 2024Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorial12 Feb
  9. 2024Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distances31 Jan
  10. 2023DPM-Solver-v3: Improved Diffusion ODE Solver with Empirical Model Statistics20 Oct
  11. 2023SA-Solver: Stochastic Adams Solver for Fast Sampling of Diffusion Models10 Sep
  12. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  13. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models15 Jun
  14. 2023Parallel Sampling of Diffusion Models25 May
  15. 2023The probability flow ODE is provably fast19 May
  16. 2023Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers6 Mar
  17. 2023Consistency Models2 Mar
  18. 2023UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models9 Feb
  19. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  20. 2022DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models2 Nov
  21. 2022On Distillation of Guided Diffusion Models6 Oct
  22. 2022Convergence of score-based generative modeling for general data distributions26 Sep
  23. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  24. 2022Diffusion Models in Vision: A Survey10 Sep
  25. 2022Diffusion Models: A Comprehensive Survey of Methods and Applications2 Sep
  26. 2022Let us Build Bridges: Understanding and Extending Diffusion Generative Models31 Aug
  27. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  28. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  29. 2021Gotta Go Fast When Generating Data with Score-Based Models28 May
  30. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  31. 2021Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed7 Jan
  32. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  33. 2020Denoising Diffusion Implicit Models6 Oct
  34. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 3

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  2. 2022Generative Adversarial Networkscited by 5,627
  3. 2023Convergence of flow-based generative models via proximal gradient descent in Wasserstein spacecited by 34

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 5; 2026: 11.

16 papers.

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  1. 2026Confidence-Based Decoding is Provably Efficient for Diffusion Language Modelscited by 18
  2. 2025Optimal Convergence Analysis of DDPM for General Distributionscited by 16
  3. 2026High-accuracy sampling for diffusion models and log-concave distributionscited by 16
  4. 2026Adaptation to Intrinsic Dependence in Diffusion Language Modelscited by 10
  5. 2025Towards a unified framework for guided diffusion modelscited by 8
  6. 2026High-accuracy and dimension-free sampling with diffusionscited by 7
  7. 2025Dimension-free error estimate for diffusion model and optimal schedulingcited by 3
  8. 2025Simultaneous Approximation of the Score Function and Its Derivatives by Deep Neural Networkscited by 3
  9. 2026Denoising growth complexity: Data geometry and certified schedules for diffusion samplingcited by 2
  10. 2026ConvergeFlow: Language Flow with Provable Convergence to Token Embeddingscited by 2
  11. 2026Provably Reliable Classifier Guidance via Cross-Entropy Controlcited by 1
  12. 2026On the Robustness of Distribution Support under Diffusion Guidancecited by 1
4 more
  1. 2026From Scores to Gibbs Correctors: Accelerating Uniform-Rate Discrete Diffusion Modelscited by 1
  2. 2026A Quantitative Approximation Framework for Flow Distillation in Diffusion Modelscited by 1
  3. 2026Diffusion Models Adapt to Low-Dimensional Structure Under Flexible Coefficient Choicescited by 1
  4. 2025Are First-Order Diffusion Samplers Really Slower? A Fast Forward-Value Approachcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Beyond Scores: Proximal Diffusion Models
  2. 2023A Geometric Perspective on Diffusion Models
  3. 2026Diffusion Models with Heavy-Tailed Targets: Score Estimation and Sampling Guarantees
  4. 2026Diffusion Path Samplers via Sequential Monte Carlo
  5. 2026Diffusion Models Are Statistically Optimal for Learning Low-Dimensional Multi-Modal Distributions
  6. 2025Advancing Wasserstein Convergence Analysis of Score-Based Models: Insights from Discretization and Second-Order Acceleration
  7. 2024Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptions
  8. 2026Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees