Hyperbolic Cycle Alignment for Infrared-Visible Image Fusion

Accurate alignment is a fundamental prerequisite for multi-modal image fusion, yet aligning multi-modal remains challenging due to nonlinear geometric distortions and substantial appearance discrepancies. This work presents the Hyperbolic Cycle Alignment Network (Hy-CycleAlign), a geometry-aware cyclic alignment framework formulated in hyperbolic space. By embedding multi-level representations into a negatively curved manifold, Hy-CycleAlign departs from conventional Euclidean-space paradigms and provides enhanced sensitivity to spatial perturbations, enabling more reliable modeling of cross-modal correspondences. The framework integrates a dual-path cyclic structure that enforces bidirectional deformation consistency and prevents accumulated alignment drift. In addition, a hyperbolic hierarchy contrastive alignment module jointly constrains semantic and structural representations within a unified hyperbolic embedding domain, promoting coherent alignment across global and local geometric scales. From a theoretical standpoint, we derive the sensitivity properties of the Poincaré model and show that its metric inherently amplifies positional variations, thereby strengthening the discriminability of subtle cross-modal misalignments compared with Euclidean geometry. Extensive experiments on diverse misaligned multi-modal datasets show that Hy-CycleAlign achieves strong overall results in alignment accuracy, structural fidelity, and downstream fusion quality. These results validate the effectiveness of hyperbolic geometric modeling for robust multi-modal image alignment.