# Generalization error bound for denoising score matching under relaxed manifold assumption

arXiv: https://arxiv.org/abs/2502.13662 · HTML: https://mlsanity.com/paper/2502.13662/

## Key facts

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

## Built on by (most cited first, 20 of 20)

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- [Statistical Convergence of Spherical First Hitting Diffusion Models](https://mlsanity.com/paper/2605.07625/) (2026)
- [Finite Sample Bounds for Learning with Score Matching](https://mlsanity.com/paper/2605.14168/) (2026)
- [Sufficient Dimesion Reduction via Generalized Stein's Lemma](https://mlsanity.com/paper/2608.15121/) (2026)
- [Robustness of Diffusion Models under Distribution Shift](https://mlsanity.com/paper/2609.27546/) (2026)
- [Flow Matching under Noisy Latent Structure: Beyond Exact Low-Dimensional Support](https://mlsanity.com/paper/2609.38918/) (2026)
- [A Stochastic Analysis Perspective on Diffusion Models](https://mlsanity.com/paper/2610.14133/) (2026)

## 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.