Optimal Denoising in Score-Based Generative Models: The Role of Data Regularity
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918392434262016 |
|---|---|
| author | Beyler, Eliot Bach, Francis |
| author_facet | Beyler, Eliot Bach, Francis |
| contents | Score-based generative models achieve state-of-the-art sampling performance by denoising a distribution perturbed by Gaussian noise. In this paper, we focus on a single deterministic denoising step, and compare the optimal denoiser for the quadratic loss, we name ''full-denoising'', to the alternative ''half-denoising'' introduced by Hyv{ä}rinen (2025). We show that looking at the performance in terms of distance between distributions tells a more nuanced story, with different assumptions on the data leading to very different conclusions. We prove that half-denoising is better than full-denoising for regular enough densities, while full-denoising is better for singular densities such as mixtures of Dirac measures or densities supported on a low-dimensional subspace. In the latter case, we prove that full-denoising can alleviate the curse of dimensionality under a linear manifold hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12966 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Denoising in Score-Based Generative Models: The Role of Data Regularity Beyler, Eliot Bach, Francis Machine Learning Score-based generative models achieve state-of-the-art sampling performance by denoising a distribution perturbed by Gaussian noise. In this paper, we focus on a single deterministic denoising step, and compare the optimal denoiser for the quadratic loss, we name ''full-denoising'', to the alternative ''half-denoising'' introduced by Hyv{ä}rinen (2025). We show that looking at the performance in terms of distance between distributions tells a more nuanced story, with different assumptions on the data leading to very different conclusions. We prove that half-denoising is better than full-denoising for regular enough densities, while full-denoising is better for singular densities such as mixtures of Dirac measures or densities supported on a low-dimensional subspace. In the latter case, we prove that full-denoising can alleviate the curse of dimensionality under a linear manifold hypothesis. |
| title | Optimal Denoising in Score-Based Generative Models: The Role of Data Regularity |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2503.12966 |