Explain near-100% constraint violations by diffusion models in EngiBench experiments

Determine why the conditional diffusion models (CDiffusion2D) used for inverse design in the EngiBench cross-domain study produced samples that violated problem constraints almost 100% of the time on constrained tasks such as Beams2D and HeatConduction2D, as measured by the Ratio of Violated Constraints (RVC) metric.

Background

The paper evaluates generative models—an unconditional GAN (GAN2D), a conditional GAN (CGAN2D), and a conditional diffusion model (CDiffusion2D)—across multiple EngiBench problems, including Beams2D and HeatConduction2D, which impose explicit feasibility constraints (e.g., volume fraction limits).

While some models achieved reasonable similarity and optimality metrics, the diffusion-based model exhibited an unusually high rate of constraint violations, reflected by a near-100% Ratio of Violated Constraints (RVC) in the reported results. The authors explicitly note they did not extensively tune hyperparameters, but they state that the reason for this failure mode remains unclear, making it an open question for future investigation.