# Constraining Generative Models for Engineering Design with Negative Data

arXiv: https://arxiv.org/abs/2306.15166 · HTML: https://mlsanity.com/paper/2306.15166/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 95 references that are in the map.
- First posted on arXiv 27 Jun 2023.

## Builds on (most cited first, 30 of 40)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning](https://mlsanity.com/paper/1705.07761/) (2017)
- [Learning in Implicit Generative Models](https://mlsanity.com/paper/1610.03483/) (2016)
- [Telescoping Density-Ratio Estimation](https://mlsanity.com/paper/2006.12204/) (2020)
- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Diffusion Models Beat GANs on Topology Optimization](https://mlsanity.com/paper/2208.09591/) (2022)
- [SketchGen: Generating Constrained CAD Sketches](https://mlsanity.com/paper/2106.02711/) (2021)
- [Vitruvion: A Generative Model of Parametric CAD Sketches](https://mlsanity.com/paper/2109.14124/) (2021)
- [TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain](https://mlsanity.com/paper/2003.04685/) (2020)
- [Density Ratio Estimation via Infinitesimal Classification](https://mlsanity.com/paper/2111.11010/) (2021)
- [Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems](https://mlsanity.com/paper/2006.15274/) (2020)
- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [Negative Data Augmentation](https://mlsanity.com/paper/2102.05113/) (2021)
- [Relational inductive bias for physical construction in humans and machines](https://mlsanity.com/paper/1806.01203/) (2018)
- [Deep learning for determining a near-optimal topological design without any iteration](https://mlsanity.com/paper/1801.05463/) (2018)
- [Reconstruction of three-dimensional porous media using generative adversarial neural networks](https://mlsanity.com/paper/1704.03225/) (2017)
- [On the use of Artificial Neural Networks in Topology Optimisation](https://mlsanity.com/paper/2208.02563/) (2022)
- [PcDGAN: A Continuous Conditional Diverse Generative Adversarial Network For Inverse Design](https://mlsanity.com/paper/2106.03620/) (2021)
- [GDPP: Learning Diverse Generations Using Determinantal Point Process](https://mlsanity.com/paper/1812.00068/) (2018)
- [Topology Optimization via Machine Learning and Deep Learning: A Review](https://mlsanity.com/paper/2210.10782/) (2022)
- [Beyond Statistical Similarity: Rethinking Metrics for Deep Generative Models in Engineering Design](https://mlsanity.com/paper/2302.02913/) (2023)
- [MO-PaDGAN: Reparameterizing Engineering Designs for Augmented Multi-objective Optimization](https://mlsanity.com/paper/2009.07110/) (2020)
- [IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures](https://mlsanity.com/paper/2103.02588/) (2021)
- [3D Shape Synthesis for Conceptual Design and Optimization Using Variational Autoencoders](https://mlsanity.com/paper/1904.07964/) (2019)

## Built on by (most cited first, 11 of 11)

- [Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints](https://mlsanity.com/paper/2506.04171/) (2025)
- [On the Challenges and Opportunities in Generative AI](https://mlsanity.com/paper/2403.00025/) (2024)
- [ShipGen: A Diffusion Model for Parametric Ship Hull Generation with Multiple Objectives and Constraints](https://mlsanity.com/paper/2311.06315/) (2023)
- [Don't be so negative! Score-based Generative Modeling with Oracle-assisted Guidance](https://mlsanity.com/paper/2307.16463/) (2023)
- [BikeBench: A Bicycle Design Benchmark for Generative Models with Objectives and Constraints](https://mlsanity.com/paper/2508.00830/) (2025)
- [Scorecards for Synthetic Medical Data Evaluation and Reporting](https://mlsanity.com/paper/2406.11143/) (2024)
- [C-ShipGen: A Conditional Guided Diffusion Model for Parametric Ship Hull Design](https://mlsanity.com/paper/2407.03333/) (2024)
- [CAD-Prompted Generative Models: A Pathway to Feasible and Novel Engineering Designs](https://mlsanity.com/paper/2407.08675/) (2024)
- [GLUE: Coordinating Pre-Trained Generative Models for System-Level Design](https://mlsanity.com/paper/2512.19469/) (2025)
- [FLARE: A Data-Efficient Surrogate for Predicting Displacement Fields in Directed Energy Deposition](https://mlsanity.com/paper/2604.16649/) (2026)
- [Integration Matters: Rollout-Based Training for Constrained Diffusion Models](https://mlsanity.com/paper/2607.14398/) (2026)

## Abstract (arXiv)

Generative models have recently achieved remarkable success and widespread adoption in society, yet they often struggle to generate realistic and accurate outputs. This challenge extends beyond language and vision into fields like engineering design, where safety-critical engineering standards and non-negotiable physical laws tightly constrain what outputs are considered acceptable. In this work, we introduce a novel training method to guide a generative 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 many constraint-violating samples using 1/8 as much data in certain problems. It also consistently outperforms other baselines, achieving a balance between constraint satisfaction and distributional similarity that is unsurpassed by any other model in 12 of the 14 problems tested. This widespread superiority is rigorously demonstrated across numerous synthetic tests and real engineering problems, such as ship hull synthesis with hydrodynamic constraints and vehicle design with impact safety constraints. Our benchmarks showcase both the best-in-class performance of our new NDGM formulation and the overall dominance of NDGMs versus classic generative models. We publicly release the code and benchmarks at https://github.com/Lyleregenwetter/NDGMs.