Point cloud synthesis with stochastic differential equations

In this article, we propose a point cloud synthesis method based on stochastic differential equations. We view the point cloud generation process as smoothly transforming from a known prior distribution toward the high-likelihood shape by point-level denoising. We introduce a conditional corrector sampler to improve the quality of point clouds. By leveraging Markov chain Monte Carlo sample, our method can synthesize realistic point clouds. We additionally prove that our approach can be trained in an auto-encoding fashion and reconstruct the point cloud faithfully. Furthermore, our model can be extended on a downstream application of point cloud completion. Experimental results demonstrate the effectiveness and efficiency of our method.