mlsanityData to 7 Oct 2026

Statistical guarantees for denoising reflected diffusion models

arXiv 2411.01563 ↗First posted 3 Nov 2024math.ST stat.ML stat.THcited by 6

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

In recent years, denoising diffusion models have become a crucial area of research due to their abundance in the rapidly expanding field of generative AI. While recent statistical advances have delivered explanations for the generation ability of idealised denoising diffusion models for high-dimensional target data, implementations introduce thresholding procedures for the generating process to overcome issues arising from the unbounded state space of such models. This mismatch between theoretical design and implementation of diffusion models has been addressed empirically by using a reflected diffusion process as the driver of noise instead. In this paper, we study statistical guarantees of these denoising reflected diffusion models. In particular, under Sobolev smoothness assumptions, we establish rates of convergence in total variation which, up to a polylogarithmic factor, match the minimax lower bound. Our main contributions include the statistical analysis of this novel class of denoising reflected diffusion models and a refined score approximation method in both time and space, leveraging spectral decomposition and rigorous neural network analysis.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 26 of its 66 references that are in the map. First posted on arXiv 3 Nov 2024.

Builds on

26 of 66 references.

Closest ancestors · 10

Same direction, newest first

  1. 2024Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions27 Sep
  2. 2024Minimax Optimality of Score-based Diffusion Models: Beyond the Density Lower Bound Assumptions23 Feb
  3. 2023Metropolis Sampling for Constrained Diffusion Models11 Jul
  4. 2023Diffusion Models for Constrained Domains11 Apr
  5. 2023Reflected Diffusion Models10 Apr
  6. 2023Diffusion Models are Minimax Optimal Distribution Estimators3 Mar
  7. 2023Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data14 Feb
  8. 2022From Denoising Diffusions to Denoising Markov Models7 Nov
  9. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  10. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 16

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2022Generative Adversarial Networkscited by 5,603
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  4. 2015Variational Inference with Normalizing Flowscited by 2,161
  5. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  6. 2016Error bounds for approximations with deep ReLU networkscited by 567
  7. 2016f-GAN: Training Generative Neural Samplers using Variational Divergence Minimizationcited by 504
  8. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 431
  9. 2018Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionalitycited by 160
  10. 2018How Well Generative Adversarial Networks Learn Distributionscited by 78
  11. 2017Neural networks and rational functionscited by 40
  12. 2020Statistical guarantees for generative models without dominationcited by 27
4 more
  1. 2020Distribution Approximation and Statistical Estimation Guarantees of Generative Adversarial Networkscited by 23
  2. 2021Rates of convergence for density estimation with generative adversarial networkscited by 13
  3. 2022Optimal 1-Wasserstein Distance for WGANscited by 3
  4. 2024Statistical algorithms for low-frequency diffusion data: A PDE approachcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 4; 2026: 2.

6 papers.

  1. 2025Minimax Optimality of the Probability Flow ODE for Diffusion Modelscited by 23
  2. 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Boundscited by 8
  3. 2025DoubleGen: Debiased Generative Modeling of Counterfactualscited by 6
  4. 2026Reflected diffusion models adapt to low-dimensional datacited by 1
  5. 2025Model-free filtering in high dimensions via projection and score-based diffusionscited by 0
  6. 2026Statistical Convergence of Spherical First Hitting Diffusion Modelscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Diffusion Models: A Mathematical Introduction
  2. 2023To smooth a cloud or to pin it down: Guarantees and Insights on Score Matching in Denoising Diffusion Models
  3. 2024On the Asymptotic Mean Square Error Optimality of Diffusion Models
  4. 2023The Missing U for Efficient Diffusion Models
  5. 2024Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality
  6. 2023Restoration-Degradation Beyond Linear Diffusions: A Non-Asymptotic Analysis For DDIM-Type Samplers
  7. 2025Beyond Fixed Horizons: A Theoretical Framework for Adaptive Denoising Diffusions
  8. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions