Information infrastructures have formed an essential part of society since the newspaper and the telegraph ruled the world. Their growth in scale and scope accelerated significantly after digital computers emerged, bringing with them novel architectural arrangements that now include user-friendly edge-devices connected to cloud-based services across personal, local, and global networks. These new digital infrastructures constitute highly complex socio-technical systems that process, store, and transfer digital data on a global scale. Identifying the forces that govern the rapid scaling and extent in scope of digital infrastructures has turned out to be a significant challenge. In this chapter, we explore this issue of digital infrastructure innovation dynamics by considering it a case of generativity. We define generativity as from-within, inherent recursive growth in the diversity, scale, and embeddedness associated with digital infrastructures. We note that the level of generativity differentiates digital infrastructures from earlier information infrastructures of modernity such as traditional telecommunications and publishing. We argue that this generativity is a manifestation of four intertwined paradoxes associated with infrastructure development, which can be reconciled in unique ways within digital infrastructures. The four paradoxes are (1) fixity vs. variation of the underlying technologies forming the physical base; (2) stability vs. change in the technological architectures; (3) control vs. autonomy within the socio-economic contexts governing infrastructure use and development; and (4) local vs. global arrangements concerning the physical embedding of infrastructure in new use sites as it expands. We present a conceptual model that integrates the effects of these paradoxes. It is organized around dimensions that capture the tangible vs. intangible sources of infrastructural coordination as well the social vs. technical nature of infrastructural arrangements. We postulate that the ongoing interactions among the quadrants implied by these two dimensions and the continuous resolution of the four paradoxes embedded within them create the properties of emergence and complexity that drive the generativity and growth associated with digital infrastructures. An initial set of principles uniquely associated with generativity in digital infrastructures are presented, and several challenges we face in deepening our understanding of how generativity emerges from the paradoxes and drives the growth of digital infrastructures are noted.