  Due to the success of generative flows to model data distributions, they have
been explored in inverse problems. Given a pre-trained generative flow,
previous work proposed to minimize the 2-norm of the latent variables as a
regularization term. The intuition behind it was to ensure high likelihood
latent variables that produce the closest restoration. However, high-likelihood
latent variables may generate unrealistic samples as we show in our
experiments. We therefore propose a solver to directly produce high-likelihood
reconstructions. We hypothesize that our approach could make generative flows a
general purpose solver for inverse problems. Furthermore, we propose 1 x 1
coupling functions to introduce permutations in a generative flow. It has the
advantage that its inverse does not require to be calculated in the generation
process. Finally, we evaluate our method for denoising, deblurring, inpainting,
and colorization. We observe a compelling improvement of our method over prior
works.
