# Blind denoising diffusion models and the blessings of dimensionality

arXiv: https://arxiv.org/abs/2602.09639 · HTML: https://mlsanity.com/paper/2602.09639/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 30 of its 48 references that are in the map.
- First posted on arXiv 10 Feb 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)
- [Convergence of score-based generative modeling for general data distributions](https://mlsanity.com/paper/2209.12381/) (2022)
- [Robust and interpretable blind image denoising via bias-free convolutional neural networks](https://mlsanity.com/paper/1906.05478/) (2019)
- [Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser](https://mlsanity.com/paper/2007.13640/) (2020)
- [Verifying the Union of Manifolds Hypothesis for Image Data](https://mlsanity.com/paper/2207.02862/) (2022)
- [KL Convergence Guarantees for Score diffusion models under minimal data assumptions](https://mlsanity.com/paper/2308.12240/) (2023)
- [Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models](https://mlsanity.com/paper/2405.14861/) (2024)
- [Linear Convergence of Diffusion Models Under the Manifold Hypothesis](https://mlsanity.com/paper/2410.09046/) (2024)
- [Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality](https://mlsanity.com/paper/2410.18784/) (2024)
- [Is Noise Conditioning Necessary for Denoising Generative Models?](https://mlsanity.com/paper/2502.13129/) (2025)
- [Equilibrium Matching: Generative Modeling with Implicit Energy-Based Models](https://mlsanity.com/paper/2510.02300/) (2025)
- [High-accuracy sampling for diffusion models and log-concave distributions](https://mlsanity.com/paper/2602.01338/) (2026)
- [One Size Fits All: Can We Train One Denoiser for All Noise Levels?](https://mlsanity.com/paper/2005.09627/) (2020)
- [The local low-dimensionality of natural images](https://mlsanity.com/paper/1412.6626/) (2014)
- [Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Models](https://mlsanity.com/paper/2501.18863/) (2025)
- [High-accuracy and dimension-free sampling with diffusions](https://mlsanity.com/paper/2601.10708/) (2026)

## Built on by (most cited first, 9 of 9)

- [The Geometry of Noise: Why Diffusion Models Don't Need Noise Conditioning](https://mlsanity.com/paper/2602.18428/) (2026)
- [What Time Is It? How Data Geometry Makes Time Conditioning Optional for Flow Matching](https://mlsanity.com/paper/2605.08344/) (2026)
- [Beckmann Transport Models: From Autonomous Flows to One-Step Maps](https://mlsanity.com/paper/2608.01692/) (2026)
- [Generative Pseudo-Force Fields for Molecular Generation](https://mlsanity.com/paper/2605.19050/) (2026)
- [Equilibrium Forcing: Adaptive Video Generation Without Noise Conditioning](https://mlsanity.com/paper/2608.14706/) (2026)
- [On the Redundancy of Timestep Embeddings in Diffusion Models](https://mlsanity.com/paper/2606.20416/) (2026)
- [A statistical theory for blind denoising: minimax estimation of the noise level from a single sample](https://mlsanity.com/paper/2609.33008/) (2026)
- [Jumping up and down: Denoiser diffusion models for discrete ordinal data](https://mlsanity.com/paper/2610.02754/) (2026)
- [Velocity Scaling in Flow Matching](https://mlsanity.com/paper/2610.10823/) (2026)

## Abstract (arXiv)

Denoising diffusion models (DDMs) are state-of-the-art methods for learning densities from data across numerous domains, yet many aspects of the training and sampling pipeline remain poorly understood. In particular, noise conditioning requires practitioners to incorporate contrived unprincipled noise embeddings into neural network architectures and to use ad hoc noise schedules for sampling. To address these drawbacks, we provide a complete theory for blind denoising diffusion models (BDDMs): a variant of DDMs where the noise amplitude is not passed into the neural network during training or sampling, obviating the need for the aforementioned design choices. We justify the correctness of BDDMs as a sampling algorithm under an assumption of low intrinsic dimensionality of the underlying data distribution relative to the ambient dimension. This assumption arises through the introduction of the Bayesian problem of estimating noise levels from a single noisy sample, which might be of independent interest. We empirically compare the performance of BDDMs to standard DDMs, showcasing the benefits of an adaptive scheme which is rigorously justified by our analysis.