Single-pixel imaging (SPI) is an emerging imaging methodology that converts a two-or even three-dimensional image acquisition problem into a one-dimensional (1D) temporal-signal detection problem. Thus, it is crucially important to develop efficient SPI techniques for image reconstruction from the 1D measurements, in particular, an undersampled one. Recently, various studies have demonstrated the superiority of deep learning for SPI. However, due to the generalization issue, conventional datadriven deep learning is a task-specific approach. One needs to retrain the neural network for different SPI imaging problems and different types of objects. Here, we propose a variable generative network enhanced SPI algorithm (VGenNet) by incorporating a model-driven fine-tuning process into a generative model that may have been trained for other tasks. VGenNet simultaneously updates the input vector and the weights in a generator to generate feasible solutions that reproduce the raw measurements. We demonstrate the proposed technique with indoor SPI and outdoor 3D single-pixel LiDAR experiments. Our results show that high-quality images can be reconstructed at low sampling ratios under different system configurations, demonstrating the good performance and flexibility of VGenNet. Overall, the proposed VGenNet is a general framework to take advantage of both the data and physics priors, allowing the direct use of a pretrained generative model to solve various inverse imaging problems.