Satellites are emerging as promising platforms to extend generative \emph{artificial intelligence} (AI) services to remote areas lacking terrestrial infrastructure. However, deploying space generative AI is fundamentally constrained by the limited, time-varying onboard energy supplied by solar \emph{energy harvesting} (EH). This paper presents a framework for solar-powered space generative AI in which a satellite receives a user prompt, executes a diffusion-based image-generation model, and downlinks the compressed result within a strict time window. We identify the fundamental \emph{computation--communication} (C$^2$) trade-offs governed by the shared harvested-energy budgets. Specifically, increasing the number of generation steps improves intrinsic image quality but depletes energy and time available for downlink transmission, whereas prioritizing communication guarantees reliable delivery but sacrifices semantic quality. To balance these trade-offs and maximize \emph{end-to-end} (E2E) generative performance, we exploit the predictable solar-EH dynamics induced by deterministic orbital motion and develop a joint C$^2$ resource-optimization framework using a tractable two-step approach. First, we characterize the maximum downlink throughput for a fixed generation depth under continuous solar EH. This establishes a separation principle that decouples waiting-time selection from optimal transmit-power control. Next, we formulate a joint C$^2$ utility-maximization problem and derive a closed-form, low-complexity step-selection policy in the dominant constant-power regime. Extensive experiments under realistic orbital dynamics demonstrate that the proposed policy dynamically balances generation quality and transmission reliability. This yields significant E2E performance gains over static computation- and communication-centric baselines across diverse solar-EH states.

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