mlsanityData to 13 Oct 2026

Global Well-posedness and Convergence Analysis of Score-based Generative Models via Sharp Lipschitz Estimates

arXiv 2405.16104 ↗First posted 25 May 2024cs.LG math.APcited by 6

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We establish global well-posedness and convergence of the score-based generative models (SGM) under minimal general assumptions of initial data for score estimation. For the smooth case, we start from a Lipschitz bound of the score function with optimal time length. The optimality is validated by an example whose Lipschitz constant of scores is bounded at initial but blows up in finite time. This necessitates the separation of time scales in conventional bounds for non-log-concave distributions. In contrast, our follow up analysis only relies on a local Lipschitz condition and is valid globally in time. This leads to the convergence of numerical scheme without time separation. For the non-smooth case, we show that the optimal Lipschitz bound is O(1/t) in the point-wise sense for distributions supported on a compact, smooth and low-dimensional manifold with boundary.

Key facts. Cited by 6 papers in the map (data through 13 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 17 of its 35 references that are in the map. First posted on arXiv 25 May 2024.

Builds on

17 of 35 references.

Closest ancestors · 14

Same direction, newest first

  1. 2024Convergence Analysis of Probability Flow ODE for Score-based Generative Models15 Apr
  2. 2023KL Convergence Guarantees for Score diffusion models under minimal data assumptions23 Aug
  3. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  4. 2023MDTv2: Masked Diffusion Transformer is a Strong Image Synthesizer25 Mar
  5. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  6. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  7. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  8. 2022Convergence for score-based generative modeling with polynomial complexity13 Jun
  9. 2022Score-Based Generative Models Detect Manifolds2 Jun
  10. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  11. 2021Soft Truncation: A Universal Training Technique of Score-based Diffusion Model for High Precision Score Estimation10 Jun
  12. 2021Cascaded Diffusion Models for High Fidelity Image Generation30 May
2 more
  1. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov

Other references · 3

  1. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,077
  2. 2022Verifying the Union of Manifolds Hypothesis for Image Datacited by 62
  3. 2021Universal Approximation for Log-concave Distributions using Well-conditioned Normalizing Flowscited by 7

Built on by

Cited by year (2026 to 13 Oct)

Citing papers per year: 2024: 1; 2025: 2; 2026: 3.

6 papers.

  1. 2024Wasserstein Bounds for generative diffusion models with Gaussian tail targetscited by 10
  2. 2025Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Modelscited by 9
  3. 2025Pathway to O(√d) Complexity bound under Wasserstein metric of flow-based modelscited by 4
  4. 2026HybridFlow: A 2-NFE Generative Policy for Real-Time Robotic Manipulationcited by 0
  5. 2026Expressivity of Bi-Lipschitz Normalizing Flows: A Score-Based Diffusion Perspectivecited by 0
  6. 2026Probability flow ODEs in score-based and reflected diffusion modelscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates
  2. 2025Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distance
  3. 2022Convergence of score-based generative modeling for general data distributions
  4. 2025Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradients
  5. 2025Non-asymptotic error bounds for probability flow ODEs under weak log-concavity
  6. 2024An analysis of the noise schedule for score-based generative models
  7. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models
  8. 2026Intrinsic Wasserstein Rates for Score-Based Generative Models on Smooth Manifolds