The rapid growth of foundation model training and large-scale AI services has driven ground data centers toward unprecedented power densities, intensifying challenges in energy supply, cooling, and spatial scalability. Space Data Centers (SDCs) have emerged as a promising paradigm for hosting energy-intensive computing infrastructures in orbit, leveraging continuous solar energy and radiative cooling advantages. However, unlike ground facilities primarily constrained by power and site availability, SDCs are fundamentally limited by communication capability. The gap between petabit-scale internal data exchange in ground data centers and the gigabit-scale capacity of ground-space links forms a critical bottleneck. This article systematically analyzes communication constraints in SDC architectures and explores semantic communication as a key enabling paradigm. By transmitting compact, task-relevant semantic representations instead of raw data, uplink pressure can be substantially reduced. The feasibility of communication-efficient orbital AI infrastructures is demonstrated through the evaluation of a multi-layer heterogeneous SDC framework consisting of relay satellites and orbital computing nodes operating under coupled energy and thermal constraints. The article further outlines open research challenges toward scalable deployment.

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