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.