# Do Diffusion Models Dream of Electric Planes? Discrete and Continuous Simulation-Based Inference for Aircraft Design

arXiv: https://arxiv.org/abs/2603.13284 · HTML: https://mlsanity.com/paper/2603.13284/

## Key facts

- Cited by 2 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 31 of its 48 references that are in the map.
- First posted on arXiv 27 Feb 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, 30 of 31)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Unified World Models: Coupling Video and Action Diffusion for Pretraining on Large Robotic Datasets](https://mlsanity.com/paper/2504.02792/) (2025)
- [Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows](https://mlsanity.com/paper/1805.07226/) (2018)
- [Automatic Posterior Transformation for Likelihood-Free Inference](https://mlsanity.com/paper/1905.07488/) (2019)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [Approximating Likelihood Ratios with Calibrated Discriminative Classifiers](https://mlsanity.com/paper/1506.02169/) (2015)
- [Integer Discrete Flows and Lossless Compression](https://mlsanity.com/paper/1905.07376/) (2019)
- [AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions](https://mlsanity.com/paper/2212.07564/) (2022)
- [Likelihood-free inference by ratio estimation](https://mlsanity.com/paper/1611.10242/) (2016)
- [DrivAerNet++: A Large-Scale Multimodal Car Dataset with Computational Fluid Dynamics Simulations and Deep Learning Benchmarks](https://mlsanity.com/paper/2406.09624/) (2024)
- [All-in-one simulation-based inference](https://mlsanity.com/paper/2404.09636/) (2024)
- [Exponential Moving Average of Weights in Deep Learning: Dynamics and Benefits](https://mlsanity.com/paper/2411.18704/) (2024)
- [Discrete Flows: Invertible Generative Models of Discrete Data](https://mlsanity.com/paper/1905.10347/) (2019)
- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [Continuous Diffusion Model for Language Modeling](https://mlsanity.com/paper/2502.11564/) (2025)
- [Generative Modeling on Manifolds Through Mixture of Riemannian Diffusion Processes](https://mlsanity.com/paper/2310.07216/) (2023)
- [Real-time gravitational-wave inference for binary neutron stars using machine learning](https://mlsanity.com/paper/2407.09602/) (2024)
- [DeepJEB: 3D Deep Learning-based Synthetic Jet Engine Bracket Dataset](https://mlsanity.com/paper/2406.09047/) (2024)
- [BlendedNet: A Blended Wing Body Aircraft Dataset and Surrogate Model for Aerodynamic Predictions](https://mlsanity.com/paper/2509.07209/) (2025)
- [AircraftVerse: A Large-Scale Multimodal Dataset of Aerial Vehicle Designs](https://mlsanity.com/paper/2306.05562/) (2023)
- [Graphically Structured Diffusion Models](https://mlsanity.com/paper/2210.11633/) (2022)
- [Fusion of ML with numerical simulation for optimized propeller design](https://mlsanity.com/paper/2302.14740/) (2023)
- [Direct Amortized Likelihood Ratio Estimation](https://mlsanity.com/paper/2311.10571/) (2023)

## Built on by (most cited first, 2 of 2)

- [Mixed neural posterior estimation for simulators with discrete and continuous parameters](https://mlsanity.com/paper/2605.13551/) (2026)
- [Diffusion Language Models for Mobile Edge Agentic AI: Foundations, Applications, and Challenges](https://mlsanity.com/paper/2609.04778/) (2026)

## Abstract (arXiv)

In this paper, we generate conceptual engineering designs of electric vertical take-off and landing (eVTOL) aircraft. We follow the paradigm of simulation-based inference (SBI), whereby we look to learn a posterior distribution over the full eVTOL design space. To learn this distribution, we sample over discrete aircraft configurations (topologies) and their corresponding set of continuous parameters. Therefore, we introduce a hierarchical probabilistic model consisting of two diffusion models. The first model leverages recent work on Riemannian Diffusion Language Modeling (RDLM) and Unified World Models (UWMs) to enable us to sample topologies from a discrete and continuous space. For the second model we introduce a masked diffusion approach to sample the corresponding parameters conditioned on the topology. Our approach rediscovers known trends and governing physical laws in aircraft design, while significantly accelerating design generation.