mlsanityData to 14 Oct 2026

Improved Sample Complexity Bounds for Diffusion Model Training

arXiv 2311.13745 ↗First posted 23 Nov 2023cs.LG cs.CV cs.ITcited by 14

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion models have become the most popular approach to deep generative modeling of images, largely due to their empirical performance and reliability. From a theoretical standpoint, a number of recent works have studied the iteration complexity of sampling, assuming access to an accurate diffusion model. In this work, we focus on understanding the sample complexity of training such a model; how many samples are needed to learn an accurate diffusion model using a sufficiently expressive neural network? Prior work showed bounds polynomial in the dimension, desired Total Variation error, and Wasserstein error. We show an exponential improvement in the dependence on Wasserstein error and depth, along with improved dependencies on other relevant parameters.

Key facts. Cited by 14 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 24 of its 27 references that are in the map. First posted on arXiv 23 Nov 2023.

Builds on

24 of 27 references.

Closest ancestors · 15

Same direction, newest first

  1. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  2. 2023The probability flow ODE is provably fast19 May
  3. 2023Diffusion Models are Minimax Optimal Distribution Estimators3 Mar
  4. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data14 Feb
  5. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  6. 2022Convergence of score-based generative modeling for general data distributions26 Sep
  7. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  8. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  9. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  10. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  11. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  12. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
3 more
  1. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  2. 2020Denoising Diffusion Probabilistic Models19 Jun
  3. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 9

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  2. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,585
  3. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 286
  4. 2020Generative Modeling with Denoising Auto-Encoders and Langevin Samplingcited by 119
  5. 2022Improved analysis for a proximal algorithm for samplingcited by 73
  6. 2022Statistical Efficiency of Score Matching: The View from Isoperimetrycited by 64
  7. 2023Provable benefits of score matchingcited by 18
  8. 2023On Size-Independent Sample Complexity of ReLU Networkscited by 6
  9. 2023High-dimensional Location Estimation via Norm Concentration for Subgamma Vectorscited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 4; 2025: 6; 2026: 4.

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  1. 2024Faster Diffusion Sampling with Randomized Midpoints: Sequential and Parallelcited by 29
  2. 2024On the Convergence and Straightness of Rectified Flowcited by 11
  3. 2025Guiding diffusion models to reconstruct flow fields from sparse datacited by 11
  4. 2024Conditional diffusions for amortized neural posterior estimationcited by 7
  5. 2024SORSA: Singular Values and Orthonormal Regularized Singular Vectors Adaptation of Large Language Modelscited by 5
  6. 2025Discrete State Diffusion Models: A Sample Complexity Perspectivecited by 5
  7. 2025Fine-Tuning Diffusion Models via Intermediate Distribution Shapingcited by 4
  8. 2025Regularization can make diffusion models more efficientcited by 2
  9. 2025Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Accesscited by 2
  10. 2025Generative Modeling with Continuous Flows: Sample Complexity of Flow Matchingcited by 2
  11. 2026Query Lower Bounds for Diffusion Samplingcited by 2
  12. 2026Order-Optimal Sample Complexity of Rectified Flowscited by 1
2 more
  1. 2026Score Approximation for Diffusion Models on Arbitrary Low-Dimensional Structurescited by 1
  2. 2026Finite-Sample Guarantees for Fully Discrete Conditional Diffusion Modelscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023A Note on the Convergence of Denoising Diffusion Probabilistic Models
  2. 2025Convergence of Deterministic and Stochastic Diffusion-Model Samplers: A Simple Analysis in Wasserstein Distance
  3. 2024Towards Faster Training of Diffusion Models: An Inspiration of A Consistency Phenomenon
  4. 2023Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Models
  5. 2025Sparse-to-Sparse Training of Diffusion Models
  6. 2025Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics
  7. 2024Align Your Steps: Optimizing Sampling Schedules in Diffusion Models
  8. 2026Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data