Towards Computational Architecture of Liberty: A Comprehensive Survey on Deep Learning for Generating Virtual Architecture in the Metaverse

3D shape generation techniques utilizing deep learning are increasing attention from both computer vision and architectural design. This survey focuses on investigating and comparing the current latest approaches to 3D object generation with deep generative models (DGMs), including Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), 3D-aware images, and diffusion models. We discuss 187 articles (80.7% of articles published between 2018-2022) to review the field of generated possibilities of architecture in virtual environments, limited to the architecture form. We provide an overview of architectural research, virtual environment, and related technical approaches, followed by a review of recent trends in discrete voxel generation, 3D models generated from 2D images, and conditional parameters. We highlight under-explored issues in 3D generation and parameterized control that is worth further investigation. Moreover, we speculate that four research agendas including data limitation, editability, evaluation metrics, and human-computer interaction are important enablers of ubiquitous interaction with immersive systems in architecture for computer-aided design Our work contributes to researchers' understanding of the current potential and future needs of deep learnings in generating virtual architecture.