Deep generative models have shown tremendous success in data density
estimation and data generation from finite samples. While these models have
shown impressive performance by learning correlations among features in the
data, some fundamental shortcomings are their lack of explainability, the
tendency to induce spurious correlations, and poor out-of-distribution
extrapolation. In an effort to remedy such challenges, one can incorporate the
theory of causality in deep generative modeling. Structural causal models
(SCMs) describe data-generating processes and model complex causal
relationships and mechanisms among variables in a system. Thus, SCMs can
naturally be combined with deep generative models. Causal models offer several
beneficial properties to deep generative models, such as distribution shift
robustness, fairness, and interoperability. We provide a technical survey on
causal generative modeling categorized into causal representation learning and
controllable counterfactual generation methods. We focus on fundamental theory,
formulations, drawbacks, datasets, metrics, and applications of causal
generative models in fairness, privacy, out-of-distribution generalization, and
precision medicine. We also discuss open problems and fruitful research
directions for future work in the field.

深度生成模型在数据密度估计和有限样本数据生成方面取得了巨大成功。然而，它们存在无法解释性、倾向于引起虚假相关性和在超出分布范围的外推方面表现不佳等一些基本缺点。为了解决这些挑战，可以将因果性理论融入深度生成建模，结构因果模型可以描述数据生成过程并对系统中的变量之间的复杂因果关系和机制进行建模。因此，结构因果模型可以与深度生成模型自然地结合起来，给深度生成模型提供许多有益的属性，如分布偏移鲁棒性、公平性和互操作性。我们提供了一个因果生成建模的技术调研，将其分为因果表示学习和可控反事实生成方法两类。我们关注因果生成模型在公平性、隐私、超出分布泛化和精准医学方面的基本理论、形式化、缺点、数据集、度量和应用。我们还讨论了该领域未解决的问题和未来研究方向。