  Deep generative models such as Variational Autoencoders (VAEs), Generative
Adversarial Networks (GANs), Diffusion Models, and Transformers, have shown
great promise in a variety of applications, including image and speech
synthesis, natural language processing, and drug discovery. However, when
applied to engineering design problems, evaluating the performance of these
models can be challenging, as traditional statistical metrics based on
likelihood may not fully capture the requirements of engineering applications.
This paper doubles as a review and practical guide to evaluation metrics for
deep generative models (DGMs) in engineering design. We first summarize the
well-accepted `classic' evaluation metrics for deep generative models grounded
in machine learning theory. Using case studies, we then highlight why these
metrics seldom translate well to design problems but see frequent use due to
the lack of established alternatives. Next, we curate a set of design-specific
metrics which have been proposed across different research communities and can
be used for evaluating deep generative models. These metrics focus on unique
requirements in design and engineering, such as constraint satisfaction,
functional performance, novelty, and conditioning. Throughout our discussion,
we apply the metrics to models trained on simple-to-visualize 2-dimensional
example problems. Finally, we evaluate four deep generative models on a bicycle
frame design problem and structural topology generation problem. In particular,
we showcase the use of proposed metrics to quantify performance target
achievement, design novelty, and geometric constraints. We publicly release the
code for the datasets, models, and metrics used throughout the paper at
https://decode.mit.edu/projects/metrics/.
