We address the problem of cross-domain image registration, where paired images exhibit coupled geometric misalignment and domain-specific appearance shift. We formalize this as a factorization problem: decomposing each image into a domain-invariant scene representation and a global appearance statistic, such that registration reduces to recombining the scene structure of the moving image with the appearance of the fixed image via Adaptive Instance Normalization (AdaIN). This factorization eliminates the need for explicit deformation field estimation. To exploit temporal coherence in sequential acquisitions, we introduce a position-encoded cross-frame attention mechanism that fuses learnable and sinusoidal position embeddings with multi-head attention over a sliding window of neighboring frames, enriching the scene representation with inter-frame context. We instantiate this framework as GPEReg-Net and evaluate on two benchmarks: FIRE-Reg-256 (retinal fundus, semi-rigid) and HPatches-Reg-256 (synthetic textured patches, affine). GPEReg-Net achieves state-of-the-art performance on both benchmarks (FIRE: SSIM = 0.928, PSNR = 33.47 dB; HPatches: SSIM = 0.450, PSNR = 21.01 dB), surpassing all baselines, including deformation-based methods, while running 1.87x faster than SAS-Net. Code: https://github.com/JiahaoQin/GPEReg-Net.