  Diffusion models can learn strong image priors from underlying data
distribution and use them to solve inverse problems, but the training process
is computationally expensive and requires lots of data. Such bottlenecks
prevent most existing works from being feasible for high-dimensional and
high-resolution data such as 3D images. This paper proposes a method to learn
an efficient data prior for the entire image by training diffusion models only
on patches of images. Specifically, we propose a patch-based position-aware
diffusion inverse solver, called PaDIS, where we obtain the score function of
the whole image through scores of patches and their positional encoding and
utilize this as the prior for solving inverse problems. First of all, we show
that this diffusion model achieves an improved memory efficiency and data
efficiency while still maintaining the capability to generate entire images via
positional encoding. Additionally, the proposed PaDIS model is highly flexible
and can be plugged in with different diffusion inverse solvers (DIS). We
demonstrate that the proposed PaDIS approach enables solving various inverse
problems in both natural and medical image domains, including CT
reconstruction, deblurring, and superresolution, given only patch-based priors.
Notably, PaDIS outperforms previous DIS methods trained on entire image priors
in the case of limited training data, demonstrating the data efficiency of our
proposed approach by learning patch-based prior.
