用代理梯度稳定图像重建，提升逆问题求解效率与精度
P-Flow: Proxy-gradient Flows for Linear Inverse Problems
- 引入代理梯度更新源点，避免长链反向传播的数值不稳
- 在极端退化条件下（如高噪声、病态问题）仍保持优异性能
- 适合需要快速、稳定重建的图像恢复任务
基于流匹配的生成模型在逆问题中展现出强大能力，相比扩散模型具有更直的轨迹和更快的采样速度。然而，现有方法常需对展开路径进行微分，导致数值不稳定和计算开销过大。为此，我们提出P-Flow框架，通过代理梯度更新源点来稳定重建过程，有效规避长链微分带来的数值不稳与内存压力。为确保与先验分布一致，我们采用高维空间中测度集中现象启发的高斯球面投影。我们还基于贝叶斯理论和Lipschitz连续性对P-Flow进行了理论分析。在多种恢复任务上的实验表明，P-Flow在极端退化条件（如严重病态、高测量噪声）下表现尤为出色，性能具有竞争力。
原文摘要 · Abstract (English)
Generative models based on flow matching have emerged as a powerful paradigm for inverse problems, offering straighter trajectories and faster sampling compared to diffusion models. However, existing approaches often necessitate differentiating through unrolled paths, leading to numerical instability and prohibitive computational overhead. To address this, we propose P-Flow, a framework that stabilizes the reconstruction process by leveraging a proxy gradient to update the source point. This approach effectively circumvents the numerical instability and memory overhead of long-chain differentiation. To ensure consistency with the prior distribution, we employ a Gaussian spherical projection motivated by the concentration of measure phenomenon in high-dimensional spaces. We further provide a theoretical analysis for P-Flow based on Bayesian theory and Lipschitz continuity. Experiments across diverse restoration tasks demonstrate that P-Flow delivers competitive performance, especially under extreme degradations such as severely ill-posed conditions and high measurement noise.
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