Latent geometry emerging from network-driven processes

Abstract Understanding network functionality requires integrating structure and dynamics, and emergent latent geometry induced by network-driven processes captures the low-dimensional spaces governing this interplay. In this Perspective, we review generative-model-based approaches, distinguishing two reconstruction classes: fixed-time methods, which infer geometry at specific temporal scales (e.g., equilibrium), and multi-resolution methods, which integrate dynamics across near- and far-from-equilibrium states. Over the past decade, these models have revealed functional organization in biological, social, and technological networks. Hence, we provide a unified overview of these methods, with particular attention to the underlying mathematical constructions. Further, we point to promising extensions of these frameworks, which combine the previously developed methods to other well-established analytical frameworks.