A statistical theory for blind denoising: minimax estimation of the noise level from a single sample
On the map: Diffusion models → Diffusion foundations and sampling also fits: Inverse problems and image restoration
Abstract (arXiv)
Motivated by blind denoising in diffusion models, we study estimation of an unknown Gaussian noise level from a single high-dimensional observation, assuming the signal law P is known. We characterize the minimax mean-squared error under two structural assumptions on P. For signals with covering complexity k, the minimax rate is widetildeTheta_Lambda(minDelta_Lambda2,d-1+k2d-2), and the constrained MLE attains it up to logarithmic factors. For α-strongly log-concave signals, the rate is Theta_Lambda(minDelta_Lambda2,(1+α-1)2d-1), attained up to constants by a P-centered norm estimator. These results show that the structure of the signal law determines both the difficulty of blind noise estimation and the appropriate estimator.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 22 of its 36 references that are in the map. First posted on arXiv 26 Sep 2026.
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22 of 36 references.
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- 2026Blind denoising diffusion models and the blessings of dimensionality10 Feb
- 2025Is Noise Conditioning Necessary for Denoising Generative Models?18 Feb
- 2024Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality24 Oct
- 2024Linear Convergence of Diffusion Models Under the Manifold Hypothesis11 Oct
- 2024Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models23 May
- 2024Listening to the Noise: Blind Denoising with Gibbs Diffusion29 Feb
- 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
- 2022Convergence of score-based generative modeling for general data distributions26 Sep
- 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
- 2021Diffusion Models Beat GANs on Image Synthesis11 May
- 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
- 2020Denoising Diffusion Probabilistic Models19 Jun
Other references · 10
- 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
- 2022Flow Matching for Generative Modelingcited by 5,426
- 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
- 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
- 2016Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoisingcited by 1,352
- 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
- 2021The Intrinsic Dimension of Images and Its Impact on Learningcited by 307
- 2024Optimal score estimation via empirical Bayes smoothingcited by 60
- 2020One Size Fits All: Can We Train One Denoiser for All Noise Levels?cited by 10
- 2026Beckmann Transport Models: From Autonomous Flows to One-Step Mapscited by 2
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- 2025Data denoising with self consistency, variance maximization, and the Kantorovich dominance
- 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
- 2025Model-free filtering in high dimensions via projection and score-based diffusions
- 2026Robust Diffusion Models via Divergence-Induced Weighted Denoising
- 2026Precise Performance of Linear Denoisers in the Proportional Regime
- 2026Wasserstein bounds for denoising diffusion probabilistic models via the F"ollmer process