Point clouds obtained by LiDAR and other sensors are usually sparse and irregular. Low-quality point clouds have serious influence on the final performance of downstream tasks. Recently, a point cloud upsampling network with normalizing flows has been proposed to address this problem. However, the network heavily relies on designing specialized architectures to achieve invertibility. In this paper, we propose a novel invertible residual neural network for point cloud upsampling, called PU-INN, which allows unconstrained architectures to learn more expressive feature transformations. Then, we propose a conditional injector to improve nonlinear transformation ability of the neural network while guaranteeing invertibility. Furthermore, a lightweight interpolator is proposed based on semantic similarity distance in the latent space, which can intuitively reflect the interpolation changes in Euclidean space. Qualitative and quantitative results show that our method outperforms the state-of-the-art works in terms of distribution uniformity, proximity-to-surface accuracy, 3D reconstruction quality, and computation efficiency.