  Diffusion models are getting popular in generative image and video synthesis.
However, due to the diffusion process, they require a large number of steps to
converge. To tackle this issue, in this paper, we propose to perform the
diffusion process in the gradient domain, where the convergence becomes faster.
There are two reasons. First, thanks to the Poisson equation, the gradient
domain is mathematically equivalent to the original image domain. Therefore,
each diffusion step in the image domain has a unique corresponding gradient
domain representation. Second, the gradient domain is much sparser than the
image domain. As a result, gradient domain diffusion models converge faster.
Several numerical experiments confirm that the gradient domain diffusion models
are more efficient than the original diffusion models. The proposed method can
be applied in a wide range of applications such as image processing, computer
vision and machine learning tasks.
