Combining Deep Generative Models with Generalized Linear Models for Image Generation and Repair Systems: Transitioning from Statistical Modeling to Deep Learning

This study proposes a novel hybrid framework that integrates deep generative models and generalized linear models. Considering the limitation that generative models such as GAN and VAE can create realistic images but lack interpretation, we combine the statistical modeling capability of GLM with the abstract representation of deep learning by sharing the latent space. In the model architecture, the GLM branch ensures the consistency of the image structure, and the generative network is responsible for reconstructing semantic features. The two work collaboratively. The three types of random missing, center masking, and Gaussian noise degradation experiments conducted on the CelebA, cifar 10, and MNIST datasets show that this framework outperforms the single-model benchmark in terms of FID, PSNR, and SSIM metrics. Especially in medical imaging and cultural heritage restoration scenarios, the feature interpretation advantage provided by the GLM module is significant, and the influence of key parameters during the restoration process can be clearly traced. The experimental results confirm that the organic integration of statistical models and deep learning can not only improve the generation quality, but also open a new path for building reliable visual intelligence systems.