# AirfoilGen: A valid-by-construction and performance-aware latent diffusion model for airfoil generation

arXiv: https://arxiv.org/abs/2605.20303 · HTML: https://mlsanity.com/paper/2605.20303/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 20 of its 38 references that are in the map.
- First posted on arXiv 19 May 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 20 of 20)

- [Language Model Beats Diffusion -- Tokenizer is Key to Visual Generation](https://mlsanity.com/paper/2310.05737/) (2023)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [DeepCAD: A Deep Generative Network for Computer-Aided Design Models](https://mlsanity.com/paper/2105.09492/) (2021)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning](https://mlsanity.com/paper/1705.07761/) (2017)
- [MeshDiffusion: Score-based Generative 3D Mesh Modeling](https://mlsanity.com/paper/2303.08133/) (2023)
- [Octree Generating Networks: Efficient Convolutional Architectures for High-resolution 3D Outputs](https://mlsanity.com/paper/1703.09438/) (2017)
- [XCube: Large-Scale 3D Generative Modeling using Sparse Voxel Hierarchies](https://mlsanity.com/paper/2312.03806/) (2023)
- [Single-Stage Diffusion NeRF: A Unified Approach to 3D Generation and Reconstruction](https://mlsanity.com/paper/2304.06714/) (2023)
- [SolidGen: An Autoregressive Model for Direct B-rep Synthesis](https://mlsanity.com/paper/2203.13944/) (2022)
- [Airfoil Design Parameterization and Optimization using B'ezier Generative Adversarial Networks](https://mlsanity.com/paper/2006.12496/) (2020)
- [Data-Driven Aerospace Engineering: Reframing the Industry with Machine Learning](https://mlsanity.com/paper/2008.10740/) (2020)
- [ShipGen: A Diffusion Model for Parametric Ship Hull Generation with Multiple Objectives and Constraints](https://mlsanity.com/paper/2311.06315/) (2023)
- [NeuralFoil: An Airfoil Aerodynamics Analysis Tool Using Physics-Informed Machine Learning](https://mlsanity.com/paper/2503.16323/) (2025)
- [Bringing Attention to CAD: Boundary Representation Learning via Transformer](https://mlsanity.com/paper/2504.07134/) (2025)
- [Airfoil Diffusion: Denoising Diffusion Model For Conditional Airfoil Generation](https://mlsanity.com/paper/2408.15898/) (2024)
- [Intelligent CAD 2.0](https://mlsanity.com/paper/2410.03759/) (2024)
- [Push-pull direct modeling of solid CAD models](https://mlsanity.com/paper/1811.04036/) (2018)
- [Generative Aerodynamic Design with Diffusion Probabilistic Models](https://mlsanity.com/paper/2409.13328/) (2024)

## Abstract (arXiv)

Airfoil shape design is a fundamental task in aerospace engineering, with a direct impact on flight stability and fuel consumption. Deep learning has recently emerged as a promising tool for this task, but existing deep generative approaches remain limited in both geometric validity and physical controllability. They offer little control over the generated shapes, yielding invalid geometries, and they typically do not condition effectively on aerodynamic performance. To address these issues, this paper proposes AirfoilGen, a valid-by-construction and performance-aware latent diffusion model for airfoil. It first introduces a novel airfoil representation scheme, the circle sweeping representation, to constrain the generative process so that output shapes respect essential airfoil characteristics. It then enables explicit control over aerodynamic performance (e.g., lift and drag coefficients) by operating in a learned latent space: a transformer model encodes airfoil shapes into vector embeddings, and a conditional diffusion model denoises Gaussian noise into these latent embeddings while incorporating target aerodynamic performance. In addition, this paper presents a new dataset of over 200,000 airfoils, which is substantially larger than the widely used UIUC airfoil dataset (1,650 airfoils) and more suitable for training modern deep generative models. Experiments demonstrate that AirfoilGen enables airfoil generation with far greater geometric validity and aerodynamic performance controllability than previously achievable, with an average performance-conditioning accuracy of 98.41%.