# Generative Aerodynamic Design with Diffusion Probabilistic Models

arXiv: https://arxiv.org/abs/2409.13328 · HTML: https://mlsanity.com/paper/2409.13328/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 14 of its 32 references that are in the map.
- First posted on arXiv 20 Sep 2024.

## 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, 14 of 14)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [Diffusion-SDF: Conditional Generative Modeling of Signed Distance Functions](https://mlsanity.com/paper/2211.13757/) (2022)
- [Diffusion Models Beat GANs on Topology Optimization](https://mlsanity.com/paper/2208.09591/) (2022)
- [Improved Adversarial Systems for 3D Object Generation and Reconstruction](https://mlsanity.com/paper/1707.09557/) (2017)
- [Stabilizing Generative Adversarial Networks: A Survey](https://mlsanity.com/paper/1910.00927/) (2019)
- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Geometry-Complete Diffusion for 3D Molecule Generation and Optimization](https://mlsanity.com/paper/2302.04313/) (2023)
- [Airfoil Design Parameterization and Optimization using B'ezier Generative Adversarial Networks](https://mlsanity.com/paper/2006.12496/) (2020)
- [Tailoring Generative Adversarial Networks for Smooth Airfoil Design](https://mlsanity.com/paper/2404.11816/) (2024)

## Built on by (most cited first, 3 of 3)

- [Adjoint-Based Aerodynamic Shape Optimization with a Manifold Constraint Learned by Diffusion Models](https://mlsanity.com/paper/2507.23443/) (2025)
- [Efficient Diffusion Models under Nonconvex Equality and Inequality constraints via Landing](https://mlsanity.com/paper/2604.17838/) (2026)
- [AirfoilGen: A valid-by-construction and performance-aware latent diffusion model for airfoil generation](https://mlsanity.com/paper/2605.20303/) (2026)

## Abstract (arXiv)

The optimization of geometries for aerodynamic design often relies on a large number of expensive simulations to evaluate and iteratively improve the geometries. It is possible to reduce the number of simulations by providing a starting geometry that has properties close to the desired requirements, often in terms of lift and drag, aerodynamic moments and surface areas. We show that generative models have the potential to provide such starting geometries by generalizing geometries over a large dataset of simulations. In particular, we leverage diffusion probabilistic models trained on XFOIL simulations to synthesize two-dimensional airfoil geometries conditioned on given aerodynamic features and constraints. The airfoils are parameterized with Bernstein polynomials, ensuring smoothness of the generated designs. We show that the models are able to generate diverse candidate designs for identical requirements and constraints, effectively exploring the design space to provide multiple starting points to optimization procedures. However, the quality of the candidate designs depends on the distribution of the simulated designs in the dataset. Importantly, the geometries in this dataset must satisfy other requirements and constraints that are not used in conditioning of the diffusion model, to ensure that the generated geometries are physical.