The fusion of artificial intelligence (AI) and space technologies is extending spaceborne intelligence beyond onboard payloads toward a global infrastructure, here termed Space AI infrastructure (SpaceAI-Infra). Its promise rests on two distinctive advantages of space systems: abundant solar energy in orbit and the global reach of satellite constellations. Realizing this promise hinges on a fundamental systems question: How should satellite constellations be designed and orchestrated to deliver data-center-scale AI services competitive with their terrestrial counterparts? This article develops a roadmap-oriented answer. We first chart the evolution of SpaceAI-Infra through three progressive stages: onboard AI, Space Edge AI, and Space Cloud AI. By revisiting the space-constrained fundamentals for end-to-end token services, we derive enabling design principles and translate them into an integrated space edge--cloud architecture. The communication-centric space edge comprises free-flying LEO constellations that provide user-proximate computing and form the access and backhaul fabric for cloud AI services. Complementing the edge, the computing-centric space cloud comprises formation-flying satellite constellations organized as space data centers in dawn--dusk sun-synchronous orbits. A case study demonstrates that the proposed architecture can support data-center-scale foundation-model inference for millions of concurrent users worldwide.

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