Interactive applications have experienced significant growth in recent years. The rapid development of low Earth orbit (LEO) satellite networks (LSNs) providing global coverage has ushered in a new era of remote interactive applications. Yet, the dynamic nature of LSNs often mismatch the requirements of interactive video streaming for high bandwidth and low latency. Motivated by the recent advancements in generative artificial intelligence (GenAI) and satellite computing, we suggest a space generation-aware interactive video streaming framework over LSNs. We closely examine the potential and challenges of integrating GenAI with satellite computing, highlight key design issues toward its implementation, and demonstrate its effectiveness through a prototype study and large-scale simulations.