mlsanityData to 7 Oct 2026

Analysis of learning a flow-based generative model from limited sample complexity

arXiv 2310.03575 ↗First posted 5 Oct 2023stat.ML cs.LGcited by 38

Not on the map. Why?

Cited by 30 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

We study the problem of training a flow-based generative model, parametrized by a two-layer autoencoder, to sample from a high-dimensional Gaussian mixture. We provide a sharp end-to-end analysis of the problem. First, we provide a tight closed-form characterization of the learnt velocity field, when parametrized by a shallow denoising auto-encoder trained on a finite number n of samples from the target distribution. Building on this analysis, we provide a sharp description of the corresponding generative flow, which pushes the base Gaussian density forward to an approximation of the target density. In particular, we provide closed-form formulae for the distance between the mean of the generated mixture and the mean of the target mixture, which we show decays as Thetan(frac1n). Finally, this rate is shown to be in fact Bayes-optimal.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). Builds on 36 of its 44 references that are in the map. First posted on arXiv 5 Oct 2023.

Builds on

36 of 44 references.

References · 36

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  4. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  5. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  6. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  7. 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
  8. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  9. 2022Flow Matching for Generative Modelingcited by 5,426
  10. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  11. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  12. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
24 more
  1. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  2. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  3. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  4. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 440
  5. 2022Convergence of denoising diffusion models under the manifold hypothesiscited by 237
  6. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptionscited by 215
  7. 2018Statistical Aspects of Wasserstein Distancescited by 202
  8. 2022Convergence of score-based generative modeling for general data distributionscited by 179
  9. 2022Convergence for score-based generative modeling with polynomial complexitycited by 176
  10. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Datacited by 171
  11. 2023Diffusion Models are Minimax Optimal Distribution Estimatorscited by 159
  12. 2023The probability flow ODE is provably fastcited by 145
  13. 2022Score-Based Generative Models Detect Manifoldscited by 121
  14. 2020Generative Modeling with Denoising Auto-Encoders and Langevin Samplingcited by 118
  15. 2023Error Bounds for Flow Matching Methodscited by 88
  16. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Modelscited by 84
  17. 2019A Wasserstein-type distance in the space of Gaussian Mixture Modelscited by 75
  18. 2023Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplerscited by 73
  19. 2023Learning Mixtures of Gaussians Using the DDPM Objectivecited by 56
  20. 2023Reward-Directed Conditional Diffusion: Provable Distribution Estimation and Reward Improvementcited by 49
  21. 2017Optimal transport for Gaussian mixture modelscited by 45
  22. 2023Deep Networks as Denoising Algorithms: Sample-Efficient Learning of Diffusion Models in High-Dimensional Graphical Modelscited by 39
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  24. 2023High-dimensional Asymptotics of Denoising Autoencoderscited by 19

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 17; 2025: 8; 2026: 13.

38 papers.

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  1. 2024Dynamical Regimes of Diffusion Modelscited by 133
  2. 2024An analytic theory of creativity in convolutional diffusion modelscited by 103
  3. 2024A Phase Transition in Diffusion Models Reveals the Hierarchical Nature of Datacited by 88
  4. 2025Why Diffusion Models Don't Memorize: The Role of Implicit Dynamical Regularization in Trainingcited by 78
  5. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Modelscited by 64
  6. 2024Optimal score estimation via empirical Bayes smoothingcited by 60
  7. 2024What does guidance do? A fine-grained analysis in a simple settingcited by 45
  8. 2024Learning general Gaussian mixtures with efficient score matchingcited by 43
  9. 2024Critical windows: non-asymptotic theory for feature emergence in diffusion modelscited by 41
  10. 2024Learning Mixtures of Gaussians Using Diffusion Modelscited by 41
  11. 2024Understanding Generalizability of Diffusion Models Requires Rethinking the Hidden Gaussian Structurecited by 38
  12. 2024A Good Score Does not Lead to A Good Generative Modelcited by 36
26 more
  1. 2024Provable Acceleration for Diffusion Models under Minimal Assumptionscited by 27
  2. 2024Convergence of Continuous Normalizing Flows for Learning Probability Distributionscited by 24
  3. 2025How Compositional Generalization and Creativity Improve as Diffusion Models are Trainedcited by 24
  4. 2025Bigger Isn't Always Memorizing: Early Stopping Overparameterized Diffusion Modelscited by 24
  5. 2025Minimax Optimality of the Probability Flow ODE for Diffusion Modelscited by 23
  6. 2025Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curvescited by 20
  7. 2024How much is a noisy image worth? Data Scaling Laws for Ambient Diffusioncited by 18
  8. 2024U-Nets as Belief Propagation: Efficient Classification, Denoising, and Diffusion in Generative Hierarchical Modelscited by 17
  9. 2025A solvable model of learning generative diffusion: theory and insightscited by 14
  10. 2024High-dimensional learning of narrow neural networkscited by 12
  11. 2026Theory of Speciation Transitions in Diffusion Models with General Class Structurecited by 7
  12. 2026A theory of learning data statistics in diffusion models, from easy to hardcited by 5
  13. 2026Dynamical Regimes of Multimodal Diffusion Modelscited by 4
  14. 2025A statistical physics framework for optimal learningcited by 3
  15. 2026Asymptotic Learning Curves for Diffusion Models with Random Features Score and Manifold Datacited by 3
  16. 2026An exact information theory of generalization phase transitions in Bayesian diffusion modelscited by 3
  17. 2026Understanding diffusion models requires rethinking (again) generalizationcited by 2
  18. 2024Phase-aware Training Schedule Simplifies Learning in Flow-Based Generative Modelscited by 1
  19. 2025Flow Matching Calibration for Simulation-Based Inference under Model Misspecificationcited by 1
  20. 2026Multi-Subspace Multi-Modal Modeling for Diffusion Models: Estimation, Convergence and Mixture of Expertscited by 1
  21. 2026The Interplay of Data Structure and Imbalance in the Learning Dynamics of Diffusion Modelscited by 1
  22. 2026Memorisation, convergence and generalisation in generative modelscited by 1
  23. 2026Double Descent and Malign Overfitting in Diffusion Modelscited by 1
  24. 2026A Quantitative Approximation Framework for Flow Distillation in Diffusion Modelscited by 0
  25. 2026Generative Bayesian Filtering for State Estimationcited by 0
  26. 2026Weighting Schedules Govern What and When Score-Based Generative Models Learn from Multimodal Datacited by 0