用逆向均值传播直接求后验均值，比传统采样更快更准。
Score-Based Variational Inference for Inverse Problems
- 通过分析逆向扩散过程的密度演化，证明可直接追踪均值路径求解后验均值。
- 提出逆向均值传播（RMP）框架，在各步最小化反向KL散度，实现高效优化。
- 相比现有方法，重建精度更高，计算复杂度更低，适合高要求逆问题应用。
基于扩散模型的逆问题求解方法通常通过得分函数生成后验样本并取均值作为解，但需多次采样，效率低。本文分析条件逆向扩散过程的概率密度演化，证明后验均值可通过追踪每一步逆向扩散的均值实现。基于此，提出逆向均值传播（RMP）框架，将目标转化为在每一步最小化反向KL散度的变分推断问题。进一步设计算法，利用得分函数与自然梯度下降优化反向KL，并在每步传播均值。实验验证了理论有效性，且在多种逆问题上优于现有方法，兼具更高重建性能与更低计算开销。
原文摘要 · Abstract (English)
Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple samples from the posterior which is time-consuming. In this work, by analyzing the probability density evolution of the conditional reverse diffusion process, we prove that the posterior mean can be achieved by tracking the mean of each reverse diffusion step. Based on that, we establish a framework termed reverse mean propagation (RMP) that targets the posterior mean directly. We show that RMP can be implemented by solving a variational inference problem, which can be further decomposed as minimizing a reverse KL divergence at each reverse step. We further develop an algorithm that optimizes the reverse KL divergence with natural gradient descent using score functions and propagates the mean at each reverse step. Experiments demonstrate the validity of the theory of our framework and show that our algorithm outperforms state-of-the-art algorithms on reconstruction performance with lower computational complexity in various inverse problems.
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