To achieve point cloud denoising, traditional methods heavily rely on geometric priors, and most learning-based approaches suffer from outliers and loss of details. Recently, the gradient-based method was proposed to estimate the gradient fields from the noisy point clouds using neural networks, and refine the position of each point according to the estimated gradient. However, the predicted gradient could fluctuate, leading to perturbed and unstable solutions, as well as a long inference time. To address these issues, we develop the momentum gradient ascent method that leverages the information of previous iterations in determining the trajectories of the points, thus improving the stability of the solution and reducing the inference time. Experiments demonstrate that the proposed method outperforms state-of-the-art approaches with a variety of point clouds, noise types, and noise levels. Code is available at: https://github.com/IndigoPurple/MAG
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