mlsanityData to 14 Oct 2026

Model Free Prediction with Uncertainty Assessment

arXiv 2405.12684 ↗First posted 21 May 2024stat.ML cs.LGcited by 3

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Deep nonparametric regression, characterized by the utilization of deep neural networks to learn target functions, has emerged as a focus of research attention in recent years. Despite considerable progress in understanding convergence rates, the absence of asymptotic properties hinders rigorous statistical inference. To address this gap, we propose a novel framework that transforms the deep estimation paradigm into a platform conducive to conditional mean estimation, leveraging the conditional diffusion model. Theoretically, we develop an end-to-end convergence rate for the conditional diffusion model and establish the asymptotic normality of the generated samples. Consequently, we are equipped to construct confidence regions, facilitating robust statistical inference. Furthermore, through numerical experiments, we empirically validate the efficacy of our proposed methodology.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 39 of its 75 references that are in the map. First posted on arXiv 21 May 2024.

Builds on

39 of 75 references.

Closest ancestors · 18

Same direction, newest first

  1. 2024Latent Schr"odinger Bridge Diffusion Model for Generative Learning20 Apr
  2. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization11 Apr
  3. 2024Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory18 Mar
  4. 2024Accelerating Convergence of Score-Based Diffusion Models, Provably6 Mar
  5. 2023Wasserstein Convergence Guarantees for a General Class of Score-Based Generative Models18 Nov
  6. 2023Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization7 Aug
  7. 2023Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models15 Jun
  8. 2023Diffusion Models are Minimax Optimal Distribution Estimators3 Mar
  9. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data14 Feb
  10. 2022From Denoising Diffusions to Denoising Markov Models7 Nov
  11. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  12. 2022Convergence of score-based generative modeling for general data distributions26 Sep
6 more
  1. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  2. 2022Convergence for score-based generative modeling with polynomial complexity13 Jun
  3. 2021Structured Denoising Diffusion Models in Discrete State-Spaces7 Jul
  4. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  6. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 21

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  2. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,355
  3. 2023Adding Conditional Control to Text-to-Image Diffusion Modelscited by 5,503
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  5. 2014Conditional Generative Adversarial Netscited by 2,162
  6. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,027
  7. 2016Distribution-Free Predictive Inference For Regressioncited by 668
  8. 2016Error bounds for approximations with deep ReLU networkscited by 574
  9. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 433
  10. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 384
  11. 2017Optimal approximation of piecewise smooth functions using deep ReLU neural networkscited by 179
  12. 2020Deep Network Approximation for Smooth Functionscited by 164
9 more
  1. 2023Non-autoregressive Conditional Diffusion Models for Time Series Predictioncited by 78
  2. 2020Distributional Random Forests: Heterogeneity Adjustment and Multivariate Distributional Regressioncited by 37
  3. 2024Convergence of Continuous Normalizing Flows for Learning Probability Distributionscited by 26
  4. 2020Distribution Approximation and Statistical Estimation Guarantees of Generative Adversarial Networkscited by 23
  5. 2024Convergence Analysis of Flow Matching in Latent Space with Transformerscited by 16
  6. 2023Deep Neural Networks for Nonparametric Interaction Models with Diverging Dimensioncited by 15
  7. 2023Testing for the Markov Property in Time Series via Deep Conditional Generative Learningcited by 9
  8. 2023Confidence and Uncertainty Assessment for Distributional Random Forestscited by 5
  9. 2018Optimal Nonparametric Inference with Two-Scale Distributional Nearest Neighborscited by 3

Built on by

Cited by year (2026 to 14 Oct)

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

3 papers.

  1. 2025Provable Sample-Efficient Transfer Learning Conditional Diffusion Models via Representation Learningcited by 5
  2. 2025Non-asymptotic convergence bound of conditional diffusion modelscited by 1
  3. 2026Conditional Diffusion for Nonparametric Instrumental Variable Quantile Regressioncited by 0

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  5. 2026DP-aware AdaLN-Zero: Taming Conditioning-Induced Heavy-Tailed Gradients in Differentially Private Diffusion
  6. 2024On Statistical Rates of Conditional Diffusion Transformers: Approximation, Estimation and Minimax Optimality
  7. 2022Non-Uniform Diffusion Models
  8. 2025Diffusion models under low-noise regime