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Generative models have recently achieved remarkable success and widespreadadoption in society, yet they often struggle to generate realistic and accurateoutputs. This challenge extends beyond language and vision into fields likeengineering design, where safety-critical engineering standards andnon-negotiable physical laws tightly constrain what outputs are consideredacceptable. In this work, we introduce a novel training method to guide agenerative model toward constraint-satisfying outputs using `negative data' --examples of what to avoid. Our negative-data generative model (NDGM)formulation easily outperforms classic models, generating 1/6 as manyconstraint-violating samples using 1/8 as much data in certain problems. Italso consistently outperforms other baselines, achieving a balance betweenconstraint satisfaction and distributional similarity that is unsurpassed byany other model in 12 of the 14 problems tested. This widespread superiority isrigorously demonstrated across numerous synthetic tests and real engineeringproblems, such as ship hull synthesis with hydrodynamic constraints and vehicledesign with impact safety constraints. Our benchmarks showcase both thebest-in-class performance of our new NDGM formulation and the overall dominanceof NDGMs versus classic generative models. We publicly release the code andbenchmarks at https://github.com/Lyleregenwetter/NDGMs.

Constraining Generative Models for Engineering Design with Negative Data