Image-based rigid 2D/3D registration is a critical technique for fluoroscopic guided surgical interventions. In recent years, some learning-based fully differentiable methods have produced beneficial outcomes while the process of feature extraction and gradient flow transmission still lack controllability and interpretability. To alleviate these problems, in this work, we propose a novel fully differentiable correlation-driven network using a dual-branch CNN-transformer encoder which enables the network to extract and separate low-frequency global features from high-frequency local features. A correlation-driven loss is further proposed for low-frequency feature and high-frequency feature decomposition based on embedded information. Besides, a training strategy that learns to approximate a convex-shape similarity function is applied in our work. We test our approach on a in-house datasetand show that it outperforms both existing fully differentiable learning-based registration approaches and the conventional optimization-based baseline.