  Deep Generative Models (DGMs) have been shown to be powerful tools for
generating tabular data, as they have been increasingly able to capture the
complex distributions that characterize them. However, to generate realistic
synthetic data, it is often not enough to have a good approximation of their
distribution, as it also requires compliance with constraints that encode
essential background knowledge on the problem at hand. In this paper, we
address this limitation and show how DGMs for tabular data can be transformed
into Constrained Deep Generative Models (C-DGMs), whose generated samples are
guaranteed to be compliant with the given constraints. This is achieved by
automatically parsing the constraints and transforming them into a Constraint
Layer (CL) seamlessly integrated with the DGM. Our extensive experimental
analysis with various DGMs and tasks reveals that standard DGMs often violate
constraints, some exceeding $95\%$ non-compliance, while their corresponding
C-DGMs are never non-compliant. Then, we quantitatively demonstrate that, at
training time, C-DGMs are able to exploit the background knowledge expressed by
the constraints to outperform their standard counterparts with up to $6.5\%$
improvement in utility and detection. Further, we show how our CL does not
necessarily need to be integrated at training time, as it can be also used as a
guardrail at inference time, still producing some improvements in the overall
performance of the models. Finally, we show that our CL does not hinder the
sample generation time of the models.
