  Designing molecules with specific properties is a long-lasting research
problem and is central to advancing crucial domains such as drug discovery and
material science. Recent advances in deep graph generative models treat
molecule design as graph generation problems which provide new opportunities
toward the breakthrough of this long-lasting problem. Existing models, however,
have many shortcomings, including poor interpretability and controllability
toward desired molecular properties. This paper focuses on new methodologies
for molecule generation with interpretable and controllable deep generative
models, by proposing new monotonically-regularized graph variational
autoencoders. The proposed models learn to represent the molecules with latent
variables and then learn the correspondence between them and molecule
properties parameterized by polynomial functions. To further improve the
intepretability and controllability of molecule generation towards desired
properties, we derive new objectives which further enforce monotonicity of the
relation between some latent variables and target molecule properties such as
toxicity and clogP. Extensive experimental evaluation demonstrates the
superiority of the proposed framework on accuracy, novelty, disentanglement,
and control towards desired molecular properties. The code is open-source at
https://anonymous.4open.science/r/MDVAE-FD2C.
