Point cloud upsampling can improve the quality of the initial point cloud, significantly enhancing the performance of downstream tasks such as classification and segmentation. Existing methods mostly focus on generating the geometric details of point clouds, neglecting noise suppression. To address this, we propose a novel network based on a conditional diffusion model, incorporating the Adaptive Noise Suppression (ANS) module, which we refer to as PDANS. The ANS module assigns weights to each point and determines the removal strategy based on these weights, reducing the impact of noisy points on the sampling process. The module first selects the neighborhood set for each point in the point cloud and performs a weighted sum between the point and its neighbors. It then adjusts the removal points based on the weighted sum, effectively mitigating the bias caused by outliers. We introduce the TreeTrans (TT) module to capture more correlated feature information. This module learns the interaction between high-level and low-level features, resulting in a more comprehensive and refined feature representation. Our results on several widely used benchmark datasets demonstrate that PDANS exhibits exceptional robustness in noisy point cloud processing and outperforms current state-of-the-art(SOTA) methods in terms of performance. Code is available at https://github.com/Baty2023/PDANS.

Markov jump processes are continuous-time stochastic processes widely used in statistical applications in the natural sciences, and more recently in machine learning. Inference for these models typically proceeds via Markov chain Monte Carlo, and can suffer from various computational challenges. In this work, we propose a novel collapsed variational inference algorithm to address this issue. Our work leverages ideas from discrete-time Markov chains, and exploits a connection between these two through an idea called uniformization. Our algorithm proceeds by marginalizing out the parameters of the Markov jump process, and then approximating the distribution over the trajectory with a factored distribution over segments of a piecewise-constant function. Unlike MCMC schemes that marginalize out transition times of a piecewise-constant process, our scheme optimizes the discretization of time, resulting in significant computational savings. We apply our ideas to synthetic data as well as a dataset of check-in recordings, where we demonstrate superior performance over state-of-the-art MCMC methods.