mlsanityData to 7 Oct 2026

An analysis of the noise schedule for score-based generative models

arXiv 2402.04650 ↗First posted 7 Feb 2024math.ST stat.ML stat.THcited by 25

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Score-based generative models (SGMs) aim at estimating a target data distribution by learning score functions using only noise-perturbed samples from the target.Recent literature has focused extensively on assessing the error between the target and estimated distributions, gauging the generative quality through the Kullback-Leibler (KL) divergence and Wasserstein distances. Under mild assumptions on the data distribution, we establish an upper bound for the KL divergence between the target and the estimated distributions, explicitly depending on any time-dependent noise schedule. Under additional regularity assumptions, taking advantage of favorable underlying contraction mechanisms, we provide a tighter error bound in Wasserstein distance compared to state-of-the-art results. In addition to being tractable, this upper bound jointly incorporates properties of the target distribution and SGM hyperparameters that need to be tuned during training. Finally, we illustrate these bounds through numerical experiments using simulated and CIFAR-10 datasets, identifying an optimal range of noise schedules within a parametric family.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 20 of its 33 references that are in the map. First posted on arXiv 7 Feb 2024.

Builds on

20 of 33 references.

Closest ancestors · 13

Same direction, newest first

  1. 2023KL Convergence Guarantees for Score diffusion models under minimal data assumptions23 Aug
  2. 2023On the Importance of Noise Scheduling for Diffusion Models26 Jan
  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. 2022Diffusion Models: A Comprehensive Survey of Methods and Applications2 Sep
  7. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  8. 2022Convergence for score-based generative modeling with polynomial complexity13 Jun
  9. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Models10 Jun
  10. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  11. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  12. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
1 more
  1. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 7

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  4. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,419
  5. 2022DiffuSeq: Sequence to Sequence Text Generation with Diffusion Modelscited by 439
  6. 2021SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Modelscited by 415
  7. 2020Generative Modeling with Denoising Auto-Encoders and Langevin Samplingcited by 118

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 11; 2026: 11.

25 papers.

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  1. 2025Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distancecited by 27
  2. 2025Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distancecited by 20
  3. 2025Advancing Wasserstein Convergence Analysis of Score-Based Models: Insights from Discretization and Second-Order Accelerationcited by 17
  4. 2025Wasserstein Convergence of Score-based Generative Models under Semiconvexity and Discontinuous Gradientscited by 15
  5. 2024Wasserstein Bounds for generative diffusion models with Gaussian tail targetscited by 10
  6. 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Boundscited by 8
  7. 2026Lipschitz regularity in Flow Matching and Diffusion Models: sharp sampling rates and functional inequalitiescited by 6
  8. 2025Wasserstein Convergence of Critically Damped Langevin Diffusionscited by 5
  9. 2025Optimal Denoising in Score-Based Generative Models: The Role of Data Regularitycited by 4
  10. 2024AsyncDSB: Schedule-Asynchronous Diffusion Schr"odinger Bridge for Image Inpaintingcited by 3
  11. 2025Kernel-Smoothed Scores for Denoising Diffusion: A Bias-Variance Studycited by 3
  12. 2025Dimension-free error estimate for diffusion model and optimal schedulingcited by 3
13 more
  1. 2026On Forgetting and Stability of Score-based Generative modelscited by 3
  2. 2026A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimationcited by 3
  3. 2025A Malliavin-Gamma calculus approach to Score Based Diffusion Generative models for random fieldscited by 2
  4. 2026Understanding diffusion models requires rethinking (again) generalizationcited by 2
  5. 2026Wasserstein bounds for denoising diffusion probabilistic models via the F"ollmer processcited by 2
  6. 2024Structural and Convergence Analysis of Discrete-Time Denoising Diffusion Probabilistic Modelscited by 1
  7. 2025Exact Evaluation of the Accuracy of Diffusion Models for Inverse Problems with Gaussian Data Distributionscited by 0
  8. 2026Do Heavy Tails Help Diffusion? On the Subtle Trade-off Between Initialization and Trainingcited by 0
  9. 2026Training-Free Generative Sampling via Moment-Matched Score Smoothingcited by 0
  10. 2026Diffusion Flow Matching: Dimension-Improved KL Bounds and Wasserstein Guaranteescited by 0
  11. 2026Tightening the Score Matching Gap for Diffusion Modelscited by 0
  12. 2026Non-asymptotic Convergence of Stochastic Gradient Descent in Score-based Generative Modelscited by 0
  13. 2026Universal Local Error and Realized Amplification for the First-Order EDM Predictorcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024A Good Score Does not Lead to A Good Generative Model
  2. 2022Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance
  3. 2025Algorithm- and Data-Dependent Generalization Bounds for Diffusion Models
  4. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models
  5. 2021Score-based Generative Modeling in Latent Space
  6. 2024Score-based generative models are provably robust: an uncertainty quantification perspective
  7. 2023Closed-Form Diffusion Models
  8. 2022On Investigating the Conservative Property of Score-Based Generative Models