Optimal Denoising in Score-Based Generative Models: The Role of Data Regularity

• URL: http://arxiv.org/abs/2503.12966v1
• Date: Mon, 17 Mar 2025 09:22:14 GMT
• Title: Optimal Denoising in Score-Based Generative Models: The Role of Data Regularity
• Authors: Eliot Beyler, Francis Bach,
• Abstract summary: We show that half-denoising is better than full-denoising for regular enough densities.<n>We prove that full-denoising can alleviate the curse of dimensionality under a linear manifold hypothesis.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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{\"a}rinen (2024). We show that looking at the performances in term of distance between distribution 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.

Related papers

• Sampling Binary Data by Denoising through Score Functions [2.9465623430708905]
  Tweedie-Miyasawa formula (TMF) is key ingredient in score-based generative models.<n>TMF ties these together via the score function of noisy data.<n>We adopt Bernoulli noise, instead of Gaussian noise, as a smoothing device.
  arXiv  Detail & Related papers  (2025-02-01T20:59:02Z)
• Realistic Noise Synthesis with Diffusion Models [44.404059914652194]
  Deep denoising models require extensive real-world training data, which is challenging to acquire.<n>We propose a novel Realistic Noise Synthesis Diffusor (RNSD) method using diffusion models to address these challenges.
  arXiv  Detail & Related papers  (2023-05-23T12:56:01Z)
• Optimizing the Noise in Self-Supervised Learning: from Importance Sampling to Noise-Contrastive Estimation [80.07065346699005]
  It is widely assumed that the optimal noise distribution should be made equal to the data distribution, as in Generative Adversarial Networks (GANs) We turn to Noise-Contrastive Estimation which grounds this self-supervised task as an estimation problem of an energy-based model of the data. We soberly conclude that the optimal noise may be hard to sample from, and the gain in efficiency can be modest compared to choosing the noise distribution equal to the data's.
  arXiv  Detail & Related papers  (2023-01-23T19:57:58Z)
• Denoising Deep Generative Models [23.19427801594478]
  Likelihood-based deep generative models have been shown to exhibit pathological behaviour under the manifold hypothesis. We propose two methodologies aimed at addressing this problem.
  arXiv  Detail & Related papers  (2022-11-30T19:00:00Z)
• The Optimal Noise in Noise-Contrastive Learning Is Not What You Think [80.07065346699005]
  We show that deviating from this assumption can actually lead to better statistical estimators. In particular, the optimal noise distribution is different from the data's and even from a different family.
  arXiv  Detail & Related papers  (2022-03-02T13:59:20Z)
• Heavy-tailed denoising score matching [5.371337604556311]
  We develop an iterative noise scaling algorithm to consistently initialise the multiple levels of noise in Langevin dynamics. On the practical side, our use of heavy-tailed DSM leads to improved score estimation, controllable sampling convergence, and more balanced unconditional generative performance for imbalanced datasets.
  arXiv  Detail & Related papers  (2021-12-17T22:04:55Z)
• Noise Distribution Adaptive Self-Supervised Image Denoising using Tweedie Distribution and Score Matching [29.97769511276935]
  We show that Tweedie distributions play key roles in modern deep learning era, leading to a distribution independent self-supervised image denoising formula without clean reference images. Specifically, by combining with the recent Noise2Score self-supervised image denoising approach and the saddle point approximation of Tweedie distribution, we can provide a general closed-form denoising formula. We show that the proposed method can accurately estimate noise models and parameters, and provide the state-of-the-art self-supervised image denoising performance in the benchmark dataset and real-world dataset.
  arXiv  Detail & Related papers  (2021-12-05T04:36:08Z)
• Neighbor2Neighbor: Self-Supervised Denoising from Single Noisy Images [98.82804259905478]
  We present Neighbor2Neighbor to train an effective image denoising model with only noisy images. In detail, input and target used to train a network are images sub-sampled from the same noisy image. A denoising network is trained on sub-sampled training pairs generated in the first stage, with a proposed regularizer as additional loss for better performance.
  arXiv  Detail & Related papers  (2021-01-08T02:03:25Z)
• Noise2Same: Optimizing A Self-Supervised Bound for Image Denoising [54.730707387866076]
  We introduce Noise2Same, a novel self-supervised denoising framework. In particular, Noise2Same requires neither J-invariance nor extra information about the noise model. Our results show that our Noise2Same remarkably outperforms previous self-supervised denoising methods.
  arXiv  Detail & Related papers  (2020-10-22T18:12:26Z)
• Generative Modeling with Denoising Auto-Encoders and Langevin Sampling [88.83704353627554]
  We show that both DAE and DSM provide estimates of the score of the smoothed population density. We then apply our results to the homotopy method of arXiv:1907.05600 and provide theoretical justification for its empirical success.
  arXiv  Detail & Related papers  (2020-01-31T23:50:03Z)
• Variational Denoising Network: Toward Blind Noise Modeling and Removal [59.36166491196973]
  Blind image denoising is an important yet very challenging problem in computer vision. We propose a new variational inference method, which integrates both noise estimation and image denoising.
  arXiv  Detail & Related papers  (2019-08-29T15:54:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.