We propose a variational inference approach to sample from the posterior distribution for solving inverse problems. From a pre-trained diffusion model, our approach trains a conditional flow model to minimize the divergence between the proposal variational distribution and the posterior distribution implicitly defined through the diffusion model. Once trained, the flow model is capable of sampling from the posterior distribution with a single NFE, amortized with respect to the measurement. The proposed method paves a new path for distilling a diffusion prior for efficient posterior sampling. We show that our method is applicable to standard signals in Euclidean space, as well as signals on manifold.

翻译：我们提出了一种变分推断方法，用于从后验分布中采样以解决逆问题。该方法基于预训练的扩散模型，训练一个条件流模型以最小化提议变分分布与通过扩散模型隐式定义的后验分布之间的散度。训练完成后，该流模型能够以单次神经函数评估（NFE）从后验分布中采样，且采样成本相对于测量值实现摊销。所提出的方法为蒸馏扩散先验以实现高效后验采样开辟了新路径。我们证明了该方法不仅适用于欧几里得空间中的标准信号，也适用于流形上的信号。