# Model-free filtering in high dimensions via projection and score-based diffusions

arXiv: https://arxiv.org/abs/2510.23197 · HTML: https://mlsanity.com/paper/2510.23197/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 56 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Builds on (most cited first, 21 of 21)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Nonparametric regression using deep neural networks with ReLU activation function](https://mlsanity.com/paper/1708.06633/) (2017)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Reflected Diffusion Models](https://mlsanity.com/paper/2304.04740/) (2023)
- [Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions](https://mlsanity.com/paper/2409.18804/) (2024)
- [Diffusion Models for Constrained Domains](https://mlsanity.com/paper/2304.05364/) (2023)
- [Blessing of dimensionality: mathematical foundations of the statistical physics of data](https://mlsanity.com/paper/1801.03421/) (2018)
- [DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transform](https://mlsanity.com/paper/2406.01781/) (2024)
- [Metropolis Sampling for Constrained Diffusion Models](https://mlsanity.com/paper/2307.05439/) (2023)
- [Statistical guarantees for generative models without domination](https://mlsanity.com/paper/2010.09237/) (2020)
- [On the minimax optimality and superiority of deep neural network learning over sparse parameter spaces](https://mlsanity.com/paper/1905.09195/) (2019)
- [A Mixture-Based Framework for Guiding Diffusion Models](https://mlsanity.com/paper/2502.03332/) (2025)
- [Nonparametric estimation of a factorizable density using diffusion models](https://mlsanity.com/paper/2501.01783/) (2025)
- [Statistical guarantees for denoising reflected diffusion models](https://mlsanity.com/paper/2411.01563/) (2024)
- [Beyond Fixed Horizons: A Theoretical Framework for Adaptive Denoising Diffusions](https://mlsanity.com/paper/2501.19373/) (2025)

## Abstract (arXiv)

We consider the problem of recovering a latent signal X from its noisy observation Y. The unknown law mathbbPX of X, and in particular its support mathscrM, are accessible only through a large sample of i.i.d. observations. We further assume mathscrM to be a low-dimensional submanifold of a high-dimensional Euclidean space ℝd. As a filter or denoiser widehat X, we suggest an estimator of the metric projection π_mathscrM(Y) of Y onto the manifold mathscrM. To compute this estimator, we study an auxiliary semiparametric model in which Y is obtained by adding isotropic Laplace noise to X. Using score matching within a corresponding diffusion model, we obtain an estimator of the Bayesian posterior mathbbPX mid Y in this setup. Our main theoretical results show that, in the limit of high dimension d, this posterior mathbbPXmid Y is concentrated near the desired metric projection π_mathscrM(Y).