Single photon counting compressive imaging, a combination of single-pixel-imaging and single-photon-counting technology, is provided with low cost and ultra-high sensitivity. However, it requires a long imaging time when applying traditional compressed sensing (CS) reconstruction algorithms. A deep-learning-based compressed reconstruction network refrains iterative computation while achieving efficient reconstruction. This paper proposes a compressed reconstruction network (OGTM) based on a generative model, adding sampling sub-network to achieve joint-optimization of sampling and generation for better reconstruction. To avoid the slow convergence caused by alternating training, initial weights of the sampling and generation sub-network are transferred from an autoencoder. The results indicate that the convergence speed and imaging quality are significantly improved. The OGTM validated on a single-photon compressive imaging system performs imaging experiments on specific and generalized targets. For specific targets, the results demonstrate that OGTM can quickly generate images from few measurements, and its reconstruction is better than the existing compressed sensing recovery algorithms, compensating defects of the generative models in compressed sensing.