  In the field of artificial intelligence (AI), the quest to understand and
model data-generating processes (DGPs) is of paramount importance. Deep
generative models (DGMs) have proven adept in capturing complex data
distributions but often fall short in generalization and interpretability. On
the other hand, causality offers a structured lens to comprehend the mechanisms
driving data generation and highlights the causal-effect dynamics inherent in
these processes. While causality excels in interpretability and the ability to
extrapolate, it grapples with intricacies of high-dimensional spaces.
Recognizing the synergistic potential, we delve into the confluence of
causality and DGMs. We elucidate the integration of causal principles within
DGMs, investigate causal identification using DGMs, and navigate an emerging
research frontier of causality in large-scale generative models, particularly
generative large language models (LLMs). We offer insights into methodologies,
highlight open challenges, and suggest future directions, positioning our
comprehensive review as an essential guide in this swiftly emerging and
evolving area.
