# FuncGenFoil: Airfoil Generation and Editing Model in Function Space

arXiv: https://arxiv.org/abs/2502.10712 · HTML: https://mlsanity.com/paper/2502.10712/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 63 references that are in the map.
- First posted on arXiv 15 Feb 2025.

## Builds on (most cited first, 30 of 33)

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- [Generative Models as Distributions of Functions](https://mlsanity.com/paper/2102.04776/) (2021)
- [Score-based Diffusion Models in Function Space](https://mlsanity.com/paper/2302.07400/) (2023)
- [Functional Flow Matching](https://mlsanity.com/paper/2305.17209/) (2023)
- [Neural Operators with Localized Integral and Differential Kernels](https://mlsanity.com/paper/2402.16845/) (2024)
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- [Diffusion Generative Models in Infinite Dimensions](https://mlsanity.com/paper/2212.00886/) (2022)
- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Infinite-Dimensional Diffusion Models](https://mlsanity.com/paper/2302.10130/) (2023)
- [Continuous-Time Functional Diffusion Processes](https://mlsanity.com/paper/2303.00800/) (2023)
- [Stochastic Process Learning via Operator Flow Matching](https://mlsanity.com/paper/2501.04126/) (2025)
- [B'ezierGAN: Automatic Generation of Smooth Curves from Interpretable Low-Dimensional Parameters](https://mlsanity.com/paper/1808.08871/) (2018)
- [Universal Functional Regression with Neural Operator Flows](https://mlsanity.com/paper/2404.02986/) (2024)

## Abstract (arXiv)

Aircraft manufacturing is the jewel in the crown of industry, in which generating high-fidelity airfoil geometries with controllable and editable representations remains a fundamental challenge. Existing deep learning methods, which typically rely on predefined parametric representations (e.g., B'ezier) or discrete point sets, face an inherent trade-off between expressive power and resolution adaptability. To tackle this challenge, we introduce FuncGenFoil, a novel function-space generative model that directly reconstructs airfoil geometries as function curves. Our method inherits the advantages of arbitrary-resolution sampling and smoothness from parametric functions, as well as the strong expressiveness of discrete point-based representations. Empirical evaluations demonstrate that FuncGenFoil improves upon state-of-the-art methods in airfoil generation, achieving a relative 74.4% reduction in label error and a 23.2% increase in diversity on the AF-200K dataset. Our results highlight the advantages of function-space modeling for aerodynamic shape optimization, offering a powerful and flexible framework for high-fidelity airfoil design.