mlsanityData to 14 Oct 2026

Wasserstein Bounds for generative diffusion models with Gaussian tail targets

arXiv 2412.11251 ↗First posted 15 Dec 2024cs.LG cs.NA math.APcited by 10

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We present an estimate of the Wasserstein distance between the data distribution and the generation of score-based generative models. The sampling complexity with respect to dimension is O(√d), with a logarithmic constant. In the analysis, we assume a Gaussian-type tail behavior of the data distribution and an ε-accurate approximation of the score. Such a Gaussian tail assumption is general, as it accommodates a practical target - the distribution from early stopping techniques with bounded support. The crux of the analysis lies in the global Lipschitz bound of the score, which is shown from the Gaussian tail assumption by a dimension-independent estimate of the heat kernel. Consequently, our complexity bound scales linearly (up to a logarithmic constant) with the square root of the trace of the covariance operator, which relates to the invariant distribution of the forward process.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 25 of its 51 references that are in the map. First posted on arXiv 15 Dec 2024.

Builds on

25 of 51 references.

Closest ancestors · 22

Same direction, newest first

  1. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions27 Sep
  2. 2024Global Well-posedness and Convergence Analysis of Score-based Generative Models via Sharp Lipschitz Estimates25 May
  3. 2024Diffusion models for Gaussian distributions: Exact solutions and Wasserstein errors23 May
  4. 2024Score-based generative models break the curse of dimensionality in learning a family of sub-Gaussian probability distributions12 Feb
  5. 2024An analysis of the noise schedule for score-based generative models7 Feb
  6. 2024Convergence Analysis for General Probability Flow ODEs of Diffusion Models in Wasserstein Distances31 Jan
  7. 2023On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates22 Nov
  8. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models18 Nov
  9. 2023KL Convergence Guarantees for Score diffusion models under minimal data assumptions23 Aug
  10. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  11. 2023Continuous-Time Functional Diffusion Processes1 Mar
  12. 2023Infinite-Dimensional Diffusion Models20 Feb
10 more
  1. 2023Score-based Diffusion Models in Function Space14 Feb
  2. 2022Diffusion Generative Models in Infinite Dimensions1 Dec
  3. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  4. 2022Convergence of score-based generative modeling for general data distributions26 Sep
  5. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  6. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  7. 2022Accelerating Diffusion Models via Early Stop of the Diffusion Process25 May
  8. 2021Conditional Image Generation with Score-Based Diffusion Models26 Nov
  9. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  10. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 3

  1. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,636
  2. 2023Projected Langevin dynamics and a gradient flow for entropic optimal transportcited by 17
  3. 2023Chain of Log-Concave Markov Chainscited by 14

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 7.

10 papers.

  1. 2025Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distancecited by 21
  2. 2025Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradientscited by 15
  3. 2026Lipschitz regularity in Flow Matching and Diffusion Models: sharp sampling rates and functional inequalitiescited by 8
  4. 2025Pathway to O(√d) Complexity bound under Wasserstein metric of flow-based modelscited by 4
  5. 2026Wasserstein bounds for denoising diffusion probabilistic models via the F"ollmer processcited by 2
  6. 2026Preconditioned One-Step Generative Modeling for Bayesian Inverse Problems in Function Spacescited by 1
  7. 2026Load--Reserve Wasserstein Propagation for Isotropic Diffusion Samplerscited by 1
  8. 2026Cold-Start Forecasting of New Product Life-Cycles via Conditional Diffusion Modelscited by 1
  9. 2026Proof-of-Authorship for Diffusion-based AI Generated Contentcited by 0
  10. 2026On the Regularity and Generalization of One-Step Wasserstein-guided Generative Models for PDE-Induced Measurescited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023A Note on the Convergence of Denoising Diffusion Probabilistic Models
  2. 2022Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance
  3. 2025Non-asymptotic error bounds for probability flow ODEs under weak log-concavity
  4. 2026From Global to Tail Convergence: Dynamics of α-Stable Score-Based Generative Models
  5. 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
  6. 2025Algorithm- and Data-Dependent Generalization Bounds for Diffusion Models
  7. 2025From Score Matching to Diffusion: A Fine-Grained Error Analysis in the Gaussian Setting
  8. 2026Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data