  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.
