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.

翻译：扩散模型在生成式图像与视频合成领域日益流行。然而，由于扩散过程本身的性质，这类模型需要大量步骤才能收敛。为解决这一问题，本文提出在梯度域中进行扩散过程，从而加速收敛。理由有二：首先，根据泊松方程，梯度域在数学上等价于原始图像域，因此图像域中的每个扩散步骤在梯度域中都有唯一对应的表示；其次，梯度域比图像域稀疏得多，这使得梯度域扩散模型收敛更快。多项数值实验证实，梯度域扩散模型在效率上优于原始扩散模型。所提出的方法可广泛应用于图像处理、计算机视觉及机器学习等各类任务。