mlsanityData to 14 Oct 2026

Generalization error bound for denoising score matching under relaxed manifold assumption

arXiv 2502.13662 ↗First posted 19 Feb 2025cs.LG math.ST stat.MLcited by 20

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Abstract (arXiv)

We examine theoretical properties of the denoising score matching estimate. We model the density of observations with a nonparametric Gaussian mixture. We significantly relax the standard manifold assumption allowing the samples step away from the manifold. At the same time, we are still able to leverage a nice distribution structure. We derive non-asymptotic bounds on the approximation and generalization errors of the denoising score matching estimate. The rates of convergence are determined by the intrinsic dimension. Furthermore, our bounds remain valid even if we allow the ambient dimension grow polynomially with the sample size.

Key facts. Cited by 20 papers in the map (data through 14 Oct 2026). First posted on arXiv 19 Feb 2025.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 6; 2026: 14.

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  1. 2026Confidence-Based Decoding is Provably Efficient for Diffusion Language Modelscited by 18
  2. 2025On the minimax optimality of Flow Matching through the connection to kernel density estimationcited by 10
  3. 2025Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Modelscited by 9
  4. 2026Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexitycited by 7
  5. 2025Distribution estimation via Flow Matching with Lipschitz guaranteescited by 6
  6. 2025Localized Diffusion Modelscited by 5
  7. 2026Diffusion Models with Heavy-Tailed Targets: Score Estimation and Sampling Guaranteescited by 5
  8. 2025Simultaneous Approximation of the Score Function and Its Derivatives by Deep Neural Networkscited by 3
  9. 2026Diffusion Models Are Statistically Optimal for Learning Low-Dimensional Multi-Modal Distributionscited by 3
  10. 2025Approximation Capabilities of Feedforward Neural Networks with GELU Activationscited by 2
  11. 2026Rao-Blackwellized Score Matching on Manifoldscited by 2
  12. 2026On the Limits of Latent Reuse in Diffusion Modelscited by 1
8 more
  1. 2026Multi-Source Transfer Learning of Sparse Single-Index Modelscited by 1
  2. 2026Non-asymptotic Convergence of Stochastic Gradient Descent in Score-based Generative Modelscited by 1
  3. 2026Statistical Convergence of Spherical First Hitting Diffusion Modelscited by 0
  4. 2026Finite Sample Bounds for Learning with Score Matchingcited by 0
  5. 2026Sufficient Dimesion Reduction via Generalized Stein's Lemmacited by 0
  6. 2026Robustness of Diffusion Models under Distribution Shiftcited by 0
  7. 2026Flow Matching under Noisy Latent Structure: Beyond Exact Low-Dimensional Supportcited by 0
  8. 2026A Stochastic Analysis Perspective on Diffusion Modelscited by 0