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

arXiv 2510.23197 ↗First posted 27 Oct 2025math.ST stat.ML stat.THcited by 0

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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).

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.

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21 of 56 references.

References · 21

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  3. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  4. 2022Classifier-Free Diffusion Guidancecited by 5,847
  5. 2021GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Modelscited by 3,614
  6. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 433
  7. 2021The Intrinsic Dimension of Images and Its Impact on Learningcited by 315
  8. 2016The Little Engine that Could: Regularization by Denoising (RED)cited by 307
  9. 2016Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applicationscited by 246
  10. 2023Reflected Diffusion Modelscited by 87
  11. 2024Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensionscited by 65
  12. 2023Diffusion Models for Constrained Domainscited by 63
9 more
  1. 2018Blessing of dimensionality: mathematical foundations of the statistical physics of datacited by 55
  2. 2024DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transformcited by 46
  3. 2023Metropolis Sampling for Constrained Diffusion Modelscited by 28
  4. 2020Statistical guarantees for generative models without dominationcited by 27
  5. 2019On the minimax optimality and superiority of deep neural network learning over sparse parameter spacescited by 24
  6. 2025A Mixture-Based Framework for Guiding Diffusion Modelscited by 18
  7. 2025Nonparametric estimation of a factorizable density using diffusion modelscited by 8
  8. 2024Statistical guarantees for denoising reflected diffusion modelscited by 6
  9. 2025Beyond Fixed Horizons: A Theoretical Framework for Adaptive Denoising Diffusionscited by 4

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  1. 2024Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models
  2. 2026Asymptotic Learning Curves for Diffusion Models with Random Features Score and Manifold Data
  3. 2026Diffusion Models Are Statistically Optimal for Learning Low-Dimensional Multi-Modal Distributions
  4. 2026Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refine
  5. 2026The Loss Floor of Denoising Score Matching: Fisher Geometry from Schr"odinger Bridges
  6. 2023Conditional score-based diffusion models for Bayesian inference in infinite dimensions
  7. 2025MAD: Manifold Attracted Diffusion
  8. 2025Low-dimensional adaptation of diffusion models: Convergence in total variation