Building on recent advances in Bayesian statistics and image denoising, we propose Noise2Score3D, a fully unsupervised framework for point cloud denoising. Noise2Score3D learns the score function of the underlying point cloud distribution directly from noisy data, eliminating the need for clean data during training. Using Tweedie's formula, our method performs denoising in a single step, avoiding the iterative processes used in existing unsupervised methods, thus improving both accuracy and efficiency. Additionally, we introduce Total Variation for Point Clouds as a denoising quality metric, which allows for the estimation of unknown noise parameters. Experimental results demonstrate that Noise2Score3D achieves state-of-the-art performance on standard benchmarks among unsupervised learning methods in Chamfer distance and point-to-mesh metrics. Noise2Score3D also demonstrates strong generalization ability beyond training datasets. Our method, by addressing the generalization issue and challenge of the absence of clean data in learning-based methods, paves the way for learning-based point cloud denoising methods in real-world applications.

New biological techniques and technological advances in high-throughput sequencing are paving the way for systematic, comprehensive annotation of many genomes, allowing differences between cell types or between disease/normal tissues to be determined with unprecedented breadth. Epigenetic modifications have been shown to exhibit rich diversity between cell types, correlate tightly with cell-type specific gene expression, and changes in epigenetic modifications have been implicated in several diseases. Previous attempts to understand chromatin state have focused on identifying combinations of epigenetic modification, but in cases of multiple cell types, have not considered the lineage of the cells in question.We present a Bayesian network that uses epigenetic modifications to simultaneously model 1) chromatin mark combinations that give rise to different chromatin states and 2) propensities for transitions between chromatin states through differentiation or disease progression. We apply our model to a recent dataset of histone modifications, covering nine human cell types with nine epigenetic modifications measured for each. Since exact inference in this model is intractable for all the scale of the datasets, we develop several variational approximations and explore their accuracy. Our method exhibits several desirable features including improved accuracy of inferring chromatin states, improved handling of missing data, and linear scaling with dataset size. The source code for our model is available at http:// http://github.com/uci-cbcl/tree-hmm.