Whitened Score Diffusion: A Structured Prior for Imaging Inverse Problems

Fuente: arXiv
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Autori principali: Alido, Jeffrey, Li, Tongyu, Sun, Yu, Tian, Lei
Natura: Preprint
Pubblicazione: 2025
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author Alido, Jeffrey
Li, Tongyu
Sun, Yu
Tian, Lei
author_facet Alido, Jeffrey
Li, Tongyu
Sun, Yu
Tian, Lei
contents 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}}.
format Preprint
id arxiv_https___arxiv_org_abs_2505_10311
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Whitened Score Diffusion: A Structured Prior for Imaging Inverse Problems
Alido, Jeffrey
Li, Tongyu
Sun, Yu
Tian, Lei
Image and Video Processing
Signal Processing
Applications
Machine Learning
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}}.
title Whitened Score Diffusion: A Structured Prior for Imaging Inverse Problems
topic Image and Video Processing
Signal Processing
Applications
Machine Learning
url https://arxiv.org/abs/2505.10311