Towards AI-Architecture Liberty: A Comprehensive Survey on Design and Generation of Virtual Architecture by Deep Learning

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 in the virtual environment. However, research on virtual architectural design remains limited, particularly regarding designer-AI collaboration and deep learning-assisted design. In our survey, we reviewed 149 related articles (81.2% of articles published between 2019 and 2023) covering architectural design, 3D shape techniques, and virtual environments. Through scrutinizing the literature, we first identify the principles of virtual architecture and illuminate its current production challenges, including datasets, multimodality, design intuition, and generative frameworks. We then introduce the latest approaches to designing and generating virtual buildings leveraging 3D shape generation and summarize four characteristics of various approaches to virtual architecture. Based on our analysis, we expound on four research agendas, including agency, communication, user consideration, and integrating tools. Additionally, we highlight four 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 designer-AI collaboration. We advocate for interdisciplinary efforts to address this timely research topic, facilitating content designing and generation in the virtual environment.