  Deep generative models like GAN and VAE have shown impressive results in
generating unconstrained objects like images. However, many design settings
arising in industrial design, material science, computer graphics and more
require that the generated objects satisfy hard combinatorial constraints or
meet objectives in addition to modeling a data distribution. To address this,
we propose GenCO, a generative framework that guarantees constraint
satisfaction throughout training by leveraging differentiable combinatorial
solvers to enforce feasibility. GenCO imposes the generative loss on provably
feasible solutions rather than intermediate soft solutions, meaning that the
deep generative network can focus on ensuring the generated objects match the
data distribution without having to also capture feasibility. This shift
enables practitioners to enforce hard constraints on the generated outputs
during end-to-end training, enabling assessments of their feasibility and
introducing additional combinatorial loss components to deep generative
training. We demonstrate the effectiveness of our approach on a variety of
generative combinatorial tasks, including game level generation, map creation
for path planning, and photonic device design, consistently demonstrating its
capability to yield diverse, high-quality solutions that verifiably adhere to
user-specified combinatorial properties.
