# PcDGAN: A Continuous Conditional Diverse Generative Adversarial Network For Inverse Design

arXiv: https://arxiv.org/abs/2106.03620 · HTML: https://mlsanity.com/paper/2106.03620/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 31 references that are in the map.
- First posted on arXiv 7 Jun 2021.

## Builds on (most cited first, 6 of 6)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [cGANs with Projection Discriminator](https://mlsanity.com/paper/1802.05637/) (2018)
- [Modulating early visual processing by language](https://mlsanity.com/paper/1707.00683/) (2017)
- [Objective-Reinforced Generative Adversarial Networks (ORGAN) for Sequence Generation Models](https://mlsanity.com/paper/1705.10843/) (2017)

## Built on by (most cited first, 30 of 30)

- [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)
- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [Multi-modal Machine Learning in Engineering Design: A Review and Future Directions](https://mlsanity.com/paper/2302.10909/) (2023)
- [Beyond Statistical Similarity: Rethinking Metrics for Deep Generative Models in Engineering Design](https://mlsanity.com/paper/2302.02913/) (2023)
- [Geometry-Informed Neural Networks](https://mlsanity.com/paper/2402.14009/) (2024)
- [ShipHullGAN: A generic parametric modeller for ship hull design using deep convolutional generative model](https://mlsanity.com/paper/2305.00210/) (2023)
- [Constraining Generative Models for Engineering Design with Negative Data](https://mlsanity.com/paper/2306.15166/) (2023)
- [t-METASET: Tailoring Property Bias of Large-Scale Metamaterial Datasets through Active Learning](https://mlsanity.com/paper/2202.10565/) (2022)
- [CCDM: Continuous Conditional Diffusion Models for Image Generation](https://mlsanity.com/paper/2405.03546/) (2024)
- [IM-Context: In-Context Learning for Imbalanced Regression Tasks](https://mlsanity.com/paper/2405.18202/) (2024)
- [Design Target Achievement Index: A Differentiable Metric to Enhance Deep Generative Models in Multi-Objective Inverse Design](https://mlsanity.com/paper/2205.03005/) (2022)
- [DATED: Guidelines for Creating Synthetic Datasets for Engineering Design Applications](https://mlsanity.com/paper/2305.09018/) (2023)
- [Turning Waste into Wealth: Leveraging Low-Quality Samples for Enhancing Continuous Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2308.10273/) (2023)
- [NITO: Neural Implicit Fields for Resolution-free Topology Optimization](https://mlsanity.com/paper/2402.05073/) (2024)
- [A Flow-Based Model for Conditional and Probabilistic Electricity Consumption Profile Generation and Prediction](https://mlsanity.com/paper/2405.02180/) (2024)
- [Exploring the Potentials and Challenges of Deep Generative Models in Product Design Conception](https://mlsanity.com/paper/2407.11104/) (2024)
- [Tailoring Generative Adversarial Networks for Smooth Airfoil Design](https://mlsanity.com/paper/2404.11816/) (2024)
- [A Reward-Directed Diffusion Framework for Generative Design Optimization](https://mlsanity.com/paper/2508.01509/) (2025)
- [Synthesizing Forestry Images Conditioned on Plant Phenotype Using a Generative Adversarial Network](https://mlsanity.com/paper/2307.03789/) (2023)
- [Conformal Predictions Enhanced Expert-guided Meshing with Graph Neural Networks](https://mlsanity.com/paper/2308.07358/) (2023)
- [A Generative Neural Network Approach for 3D Multi-Criteria Design Generation and Optimization of an Engine Mount for an Unmanned Air Vehicle](https://mlsanity.com/paper/2311.03414/) (2023)
- [Deep Generative Model-based Synthesis of Four-bar Linkage Mechanisms with Target Conditions](https://mlsanity.com/paper/2402.14882/) (2024)
- [Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects](https://mlsanity.com/paper/2605.16966/) (2026)
- [Machine learning for structure-guided materials and process design](https://mlsanity.com/paper/2312.14552/) (2023)
- [Masked Conditioning for Deep Generative Models](https://mlsanity.com/paper/2505.16725/) (2025)
- [Imbalance-Robust and Sampling-Efficient Continuous Conditional GANs via Adaptive Vicinal Learning and Auxiliary Regularization](https://mlsanity.com/paper/2508.01725/) (2025)
- [Enhancing Diffusion-Based Quantitatively Controllable Image Generation via Matrix-Form EDM and Adaptive Vicinal Training](https://mlsanity.com/paper/2602.02114/) (2026)
- [Inverse Design of Realizable Metasurface based Absorbers using Improved Conditioning and Diversity Enhanced Progressively Growing GANs](https://mlsanity.com/paper/2606.05849/) (2026)
- [DeepJEB++: Foundation Model-Driven Large-Scale 3D Engineering Dataset via 2D Latent Space Augmentation](https://mlsanity.com/paper/2606.12994/) (2026)

## Abstract (arXiv)

Engineering design tasks often require synthesizing new designs that meet desired performance requirements. The conventional design process, which requires iterative optimization and performance evaluation, is slow and dependent on initial designs. Past work has used conditional generative adversarial networks (cGANs) to enable direct design synthesis for given target performances. However, most existing cGANs are restricted to categorical conditions. Recent work on Continuous conditional GAN (CcGAN) tries to address this problem, but still faces two challenges: 1) it performs poorly on non-uniform performance distributions, and 2) the generated designs may not cover the entire design space. We propose a new model, named Performance Conditioned Diverse Generative Adversarial Network (PcDGAN), which introduces a singular vicinal loss combined with a Determinantal Point Processes (DPP) based loss function to enhance diversity. PcDGAN uses a new self-reinforcing score called the Lambert Log Exponential Transition Score (LLETS) for improved conditioning. Experiments on synthetic problems and a real-world airfoil design problem demonstrate that PcDGAN outperforms state-of-the-art GAN models and improves the conditioning likelihood by 69% in an airfoil generation task and up to 78% in synthetic conditional generation tasks and achieves greater design space coverage. The proposed method enables efficient design synthesis and design space exploration with applications ranging from CAD model generation to metamaterial selection.