mlsanityData to 14 Oct 2026

Instance-dependent Convergence Theory for Diffusion Models

arXiv 2410.13738 ↗First posted 17 Oct 2024stat.ML cs.LGcited by 21

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Score-based diffusion models have demonstrated outstanding empirical performance in machine learning and artificial intelligence, particularly in generating high-quality new samples from complex probability distributions. Improving the theoretical understanding of diffusion models, with a particular focus on the convergence analysis, has attracted significant attention. In this work, we develop a convergence rate that is adaptive to the smoothness of different target distributions, referred to as instance-dependent bound. Specifically, we establish an iteration complexity of mind,d2/3L1/3,d1/3Lvarepsilon-2/3 (up to logarithmic factors), where d denotes the data dimension, and varepsilon quantifies the output accuracy in terms of total variation (TV) distance. In addition, L represents a relaxed Lipschitz constant, which, in the case of Gaussian mixture models, scales only logarithmically with the number of components, the dimension and iteration number, demonstrating broad applicability.

Key facts. Cited by 21 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 29 of its 37 references that are in the map. First posted on arXiv 17 Oct 2024.

Builds on

29 of 37 references.

Closest ancestors · 23

Same direction, newest first

  1. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions27 Sep
  2. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models5 Aug
  3. 2024Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallel3 Jun
  4. 2024Reverse Transition Kernel: A Flexible Framework to Accelerate Diffusion Inference26 May
  5. 2024Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity24 May
  6. 2024Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models23 May
  7. 2024Convergence Analysis of Probability Flow ODE for Score-based Generative Models15 Apr
  8. 2024Accelerating Convergence of Score-Based Diffusion Models, Provably6 Mar
  9. 2024Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorial12 Feb
  10. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models18 Nov
  11. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  12. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models15 Jun
11 more
  1. 2023The probability flow ODE is provably fast19 May
  2. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  3. 2022Convergence of score-based generative modeling for general data distributions26 Sep
  4. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  5. 2022Diffusion Models in Vision: A Survey10 Sep
  6. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  7. 2022Convergence for score-based generative modeling with polynomial complexity13 Jun
  8. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  9. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  10. 2020Denoising Diffusion Implicit Models6 Oct
  11. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 6

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  2. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  3. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,355
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  5. 2022Phenaki: Variable Length Video Generation From Open Domain Textual Descriptioncited by 484
  6. 2020Efficient Learning of Generative Models via Finite-Difference Score Matchingcited by 49

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 11; 2026: 9.

21 papers.

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  1. 2025Low-dimensional adaptation of diffusion models: Convergence in total variationcited by 39
  2. 2024Provable Acceleration for Diffusion Models under Minimal Assumptionscited by 27
  3. 2025Minimax Optimality of the Probability Flow ODE for Diffusion Modelscited by 23
  4. 2025Dimension-Free Convergence of Diffusion Models for Approximate Gaussian Mixturescited by 23
  5. 2025Advancing Wasserstein Convergence Analysis of Score-Based Models: Insights from Discretization and Second-Order Accelerationcited by 17
  6. 2025Faster Diffusion Models via Higher-Order Approximationcited by 16
  7. 2026High-accuracy sampling for diffusion models and log-concave distributionscited by 16
  8. 2025Provable Efficiency of Guidance in Diffusion Models for General Data Distributioncited by 8
  9. 2025Towards a unified framework for guided diffusion modelscited by 8
  10. 2025Sublinear iterations can suffice even for DDPMscited by 7
  11. 2026High-accuracy and dimension-free sampling with diffusionscited by 7
  12. 2026Diffusion Models with Heavy-Tailed Targets: Score Estimation and Sampling Guaranteescited by 5
9 more
  1. 2026Provable diffusion-based posterior sampling for linear inverse problems via DDIMcited by 4
  2. 2025Dimension-free error estimate for diffusion model and optimal schedulingcited by 3
  3. 2026Query Lower Bounds for Diffusion Samplingcited by 2
  4. 2026ConvergeFlow: Language Flow with Provable Convergence to Token Embeddingscited by 2
  5. 2026Diffusion Models Adapt to Low-Dimensional Structure Under Flexible Coefficient Choicescited by 1
  6. 2025Diffusion Models under Alternative Noise: Simplified Analysis and Sensitivitycited by 0
  7. 2025Are First-Order Diffusion Samplers Really Slower? A Fast Forward-Value Approachcited by 0
  8. 2026Seasoning Generative Models for a Generalization Aftertastecited by 0
  9. 2026Smoothed Score Queries and the Complexity of Samplingcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis
  2. 2026Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data
  3. 2025Optimal Convergence Analysis of DDPM for General Distributions
  4. 2026Diffusion Models Are Statistically Optimal for Learning Low-Dimensional Multi-Modal Distributions
  5. 2023On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates
  6. 2024Unified Convergence Analysis for Score-Based Diffusion Models with Deterministic Samplers
  7. 2026Vocabulary-size-independent Convergence of Discrete Diffusion Models: adjoint equations induce the right space
  8. 2025Implicit Regularisation in Diffusion Models: An Algorithm-Dependent Generalisation Analysis