用高斯方法统一求解逆问题，提升图像重建质量与效率。
Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Sampling
- 引入协方差修正项改进似然近似，避免反向传播梯度。
- 在真实自然图像上实现更优的后验逼近与重建效果。
- 高效分解与求逆似然协方差矩阵，适用于多种逆问题。
扩散模型能通过建模复杂数据分布生成高质量图像，且可作为求解逆问题的有效先验。现有基于扩散的方法通常在反向采样过程中近似似然函数以融入数据一致性步骤，但此类近似要么不足，要么计算效率低。本文提出一种统一的似然近似方法，引入协方差修正项，在不传播梯度的前提下增强性能。该修正项嵌入反向扩散采样过程后，对选定分布实现了更优的后验收敛，并在真实自然图像数据集上表现更佳。此外，我们针对多种逆问题提出了高效因子分解与求逆似然协方差矩阵的方法。大量实验验证了该方法优于现有技术。代码已开源：https://github.com/CSIPlab/CoDPS。
原文摘要 · Abstract (English)
Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based methods integrate data consistency steps by approximating the likelihood function within the diffusion reverse sampling process. In this paper, we show that the existing approximations are either insufficient or computationally inefficient. To address these issues, we propose a unified likelihood approximation method that incorporates a covariance correction term to enhance the performance and avoids propagating gradients through the diffusion model. The correction term, when integrated into the reverse diffusion sampling process, achieves better convergence towards the true data posterior for selected distributions and improves performance on real-world natural image datasets. Furthermore, we present an efficient way to factorize and invert the covariance matrix of the likelihood function for several inverse problems. Our comprehensive experiments demonstrate the effectiveness of our method over several existing approaches. Code available at https://github.com/CSIPlab/CoDPS.
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