mlsanityData to 7 Oct 2026

Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access

arXiv 2505.18344 ↗First posted 23 May 2025cs.LG cs.AI stat.MLcited by 2

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion models have demonstrated state-of-the-art performance across vision, language, and scientific domains. Despite their empirical success, prior theoretical analyses of the sample complexity suffer from poor scaling with input data dimension or rely on unrealistic assumptions such as access to exact empirical risk minimizers. In this work, we provide a principled analysis of score estimation, establishing a sample complexity bound of O(ε-4). Our approach leverages a structured decomposition of the score estimation error into statistical, approximation, and optimization errors, enabling us to eliminate the exponential dependence on neural network parameters that arises in prior analyses. It is the first such result that achieves sample complexity bounds without assuming access to the empirical risk minimizer of score function estimation loss.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 47 of its 62 references that are in the map. First posted on arXiv 23 May 2025.

Builds on

47 of 62 references.

Closest ancestors · 26

Same direction, newest first

  1. 2025Bigger Isn't Always Memorizing: Early Stopping Overparameterized Diffusion Models22 May
  2. 2025Low-dimensional adaptation of diffusion models: Convergence in total variation22 Jan
  3. 2024Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality24 Oct
  4. 2024A Sharp Convergence Theory for The Probability Flow ODEs of Diffusion Models5 Aug
  5. 2024Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models23 May
  6. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization11 Apr
  7. 2024Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory18 Mar
  8. 2024Accelerating Convergence of Score-Based Diffusion Models, Provably6 Mar
  9. 2024Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptions23 Feb
  10. 2024Broadening Target Distributions for Accelerated Diffusion Models via a Novel Analysis Approach21 Feb
  11. 2024Analyzing Neural Network-Based Generative Diffusion Models through Convex Optimization3 Feb
  12. 2023Adaptive Guidance: Training-free Acceleration of Conditional Diffusion Models19 Dec
14 more
  1. 2023Improved Sample Complexity Bounds for Diffusion Model Training23 Nov
  2. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  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. 2023Universal Guidance for Diffusion Models14 Feb
  6. 2022Efficient Diffusion Models for Vision: A Survey7 Oct
  7. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  8. 2022Classifier-Free Diffusion Guidance26 Jul
  9. 2022Accelerating Diffusion Models via Early Stop of the Diffusion Process25 May
  10. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  11. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  12. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  13. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  14. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 21

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  3. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,006
  4. 2021Blended Diffusion for Text-driven Editing of Natural Imagescited by 924
  5. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 577
  6. 2022Torsional Diffusion for Molecular Conformer Generationcited by 262
  7. 2020Loss landscapes and optimization in over-parameterized non-linear systems and neural networkscited by 231
  8. 2021More Control for Free! Image Synthesis with Semantic Diffusion Guidancecited by 211
  9. 2022FastDiff: A Fast Conditional Diffusion Model for High-Quality Speech Synthesiscited by 136
  10. 2020Generative Modeling with Denoising Auto-Encoders and Langevin Samplingcited by 118
  11. 2023Diffusion Models for Reinforcement Learning: A Surveycited by 84
  12. 2024Optimal score estimation via empirical Bayes smoothingcited by 60
9 more
  1. 2019On the Sample Complexity of Actor-Critic Method for Reinforcement Learning with Function Approximationcited by 54
  2. 2020Single-Timescale Actor-Critic Provably Finds Globally Optimal Policycited by 34
  3. 2023Improved Sample Complexity Analysis of Natural Policy Gradient Algorithm with General Parameterization for Infinite Horizon Discounted Reward Markov Decision Processescited by 24
  4. 2022Bilevel Optimization with a Lower-level Contraction: Optimal Sample Complexity without Warm-startcited by 17
  5. 2024A Sharper Global Convergence Analysis for Average Reward Reinforcement Learning via an Actor-Critic Approachcited by 14
  6. 2025On The Sample Complexity Bounds In Bilevel Reinforcement Learningcited by 10
  7. 2017On the Sample Complexity of Graphical Model Selection for Non-Stationary Processescited by 3
  8. 2024Improving Molecule Generation and Drug Discovery with a Knowledge-enhanced Generative Modelcited by 3
  9. 2025PAC-Bayesian risk bounds for fully connected deep neural network with Gaussian priorscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 1.

2 papers.

  1. 2025Discrete State Diffusion Models: A Sample Complexity Perspectivecited by 4
  2. 2026D-IMPL: A Diffusion-based Solver for Parameterized BBOscited by 0

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  1. 2024Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalization
  2. 2026Diffusion Models Are Statistically Optimal for Learning Low-Dimensional Multi-Modal Distributions
  3. 2026Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Data
  4. 2026Sample complexity bounds for categorical Markov random fields via Discrete Diffusions
  5. 2026Query Lower Bounds for Diffusion Sampling
  6. 2026Quantifying Error Propagation and Model Collapse in Diffusion Models
  7. 2025Dimension-free Score Matching and Time Bootstrapping for Diffusion Models
  8. 2026Score Approximation for Diffusion Models on Arbitrary Low-Dimensional Structures