提出白化得分扩散模型，解决图像逆问题中噪声不均衡难题。
Whitened Score Diffusion: A Structured Prior for Imaging Inverse Problems
- 用白化得分函数替代传统得分，避免协方差矩阵求逆。
- 在各向异性噪声下训练的模型性能优于各向同性噪声基线。
- 适合需要结构化先验的医学成像等逆问题任务。
传统基于得分的扩散模型在各向异性高斯扩散过程中表现不佳，因其去噪得分匹配训练目标需对协方差矩阵求逆。本文提出白化得分（WS）扩散模型，一种基于随机微分方程的新框架，学习白化得分函数而非标准得分。该方法规避了协方差求逆，使扩散模型可稳定训练于任意高斯前向加噪过程。WS扩散模型在任意高斯噪声下与流匹配等价，支持定制频谱归纳偏置，并为具有结构化噪声的成像逆问题提供强贝叶斯先验。我们在CIFAR、CelebA（64×64）和CelebA-HQ（256×256）数据集上测试多种计算成像任务，结果表明：在各向异性高斯加噪过程上训练的WS扩散先验，始终优于基于各向同性高斯噪声的传统扩散先验。代码已开源。
原文摘要 · Abstract (English)
Conventional score-based diffusion models (DMs) may struggle with anisotropic Gaussian diffusion processes due to the required inversion of covariance matrices in the denoising score matching training objective \cite{vincent_connection_2011}. We propose Whitened Score (WS) diffusion models, a novel framework based on stochastic differential equations that learns the Whitened Score function instead of the standard score. This approach circumvents covariance inversion, extending score-based DMs by enabling stable training of DMs on arbitrary Gaussian forward noising processes. WS DMs establish equivalence with flow matching for arbitrary Gaussian noise, allow for tailored spectral inductive biases, and provide strong Bayesian priors for imaging inverse problems with structured noise. We experiment with a variety of computational imaging tasks using the CIFAR, CelebA ($64\times64$), and CelebA-HQ ($256\times256$) datasets and demonstrate that WS diffusion priors trained on anisotropic Gaussian noising processes consistently outperform conventional diffusion priors based on isotropic Gaussian noise. Our code is open-sourced at \href{https://github.com/jeffreyalido/wsdiffusion}{\texttt{github.com/jeffreyalido/wsdiffusion}}.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。