Towards AI-Architecture Liberty: A Comprehensive Survey on Designing and Collaborating Virtual Architecture by Deep Learning in the Metaverse

3D shape generation techniques leveraging deep learning have garnered significant interest from both the computer vision and architectural design communities, promising to enrich the content of the future metaverse. However, research on virtual architectural design remains limited, particularly regarding human-AI collaboration and deep learning-assisted design. We first illuminate the principles, generation techniques, and current literature of virtual architecture, focusing on challenges such as datasets, multimodality, design intuition, and generative frameworks. In our survey, we reviewed 187 related articles (80.7\% of articles published between 2018 and 2022) covering architectural research, virtual environments, and technical approaches. This survey investigates the latest approaches to 3D object generation with deep generative models (DGMs) and summarizes four characteristics of deep-learning generation approaches for virtual architecture. According to our analysis of the survey, we expound on four research agendas, including agency, communication, user consideration, and integrating tools, and highlight three important enablers of ubiquitous interaction with immersive systems in deep learning-assisted architectural generation. Our work contributes to fostering understanding between designers and deep learning techniques, broadening access to human-AI collaboration. We advocate for interdisciplinary efforts to address this timely research topic, facilitating content designing and generation in the metaverse.