This paper presents a novel framework for graph alignment, the problem of identifying corresponding nodes in multiple graphs. Existing unsupervised learning approaches embed node features into latent representations to perform inter-graph comparisons, but suffer from issues such as poor node discriminability and misalignment in the latent space. This study proposes a framework that improves node discriminability and enhances geometric consistency across latent spaces. The framework utilizes a double-pass encoder that combines low-pass and high-pass spectral filters to generate structure-aware, highly discriminative embeddings. Furthermore, to address latent space misalignment, it integrates a geometrically aware feature map module that learns bijective and isometric transformations between graph embeddings, ensuring consistent geometric relationships between different representations. Experiments on graph benchmarks and visual-language benchmarks using various pre-trained models demonstrate that the proposed method outperforms existing unsupervised learning-based alignment methods, demonstrating its robustness to structural misalignment. Furthermore, it demonstrates that the proposed method enables unsupervised alignment of visual and language representations beyond the graph domain.
