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

Conceptual aircraft design is traditionally an expert-mediated iterative process in which a human designer proposes a configuration, runs low-order physics, inspects the result, and re-proposes. We present AlphaJet, an end-to-end automated synthesis pipeline that closes this loop. From a textual mission specification (mass, range, cruise speed, hard size envelope, engine count, areal density) AlphaJet evolves a feasible 3D aircraft in real time, scored by a transparent multi-disciplinary fitness function covering aerodynamics, structures, weights, stability, packaging, and geometric mount consistency. Three contributions distinguish our approach: (i) an Anatomically-Disentangled Variational Autoencoder (AD-VAE) whose first 25 latent dimensions are supervised to align with named anatomical parameters, providing an interpretable shape prior; (ii) a topology-elitist genetic algorithm that protects the best individual from each of five tail topologies and triggers stagnation restarts, preventing premature collapse to a single configuration; and (iii) mount-aware geometric scoring that computes signed penetration between engines and other structural parts, eliminating the redundant artifacts common in generative aircraft models. The full loop runs interactively on a CPU and streams every generation to a browser viewer, making it a practical real-world automation tool for early-phase design-space exploration.

Diffusion models have recently emerged as powerful learners for simulation-based inference (SBI), enabling fast and accurate estimation of latent parameters from simulated and real data. Their score-based formulation offers a flexible way to learn conditional or joint distributions over parameters and observations, thereby providing a versatile solution to various modeling problems. In this tutorial review, we synthesize recent developments on diffusion models for SBI, covering design choices for training, inference, and evaluation. We highlight opportunities created by various concepts such as guidance, score composition, flow matching, consistency models, and joint modeling. Furthermore, we discuss how efficiency and statistical accuracy are affected by noise schedules, parameterizations, and samplers. Finally, we illustrate these concepts with case studies across parameter dimensionalities, simulation budgets, and model types, and outline open questions for future research.

Natural load-bearing patterns such as leaf venation, trabecular bone, and spider webs achieve high stiffness per unit mass, yet classical topology optimizers rarely reach such geometries, and few let engineers express structural design intent through natural language. This work treats a frozen text-to-image diffusion model as a training-free source of design knowledge and distills it into the physics loop of density-based topology optimization via score distillation sampling, so that a text prompt becomes an explicit, machine-interpretable representation of engineer intent. The prompt-induced generative gradient and the finite element sensitivity are combined at every iteration, letting physics decide which prompt-induced features survive. In 245 primary SDS runs spanning four geometric domains and two physics regimes, 38 of 49 prompt--domain combinations achieved statistically significant compliance reductions (up to $-31.5\%$ mechanical and $-23.0\%$ thermoelastic), outperforming gradient-based baselines. Cross-domain morphological analysis identifies a recurring structural signature of improvement: in most domains the generative prior suppresses dead-end branches in the rib skeleton, with endpoint--compliance correlation $r = +0.56$ to $+0.99$. A Heaviside projection with $β$-continuation resolves a pronounced intermediate-density tendency in this diffusion--physics coupling ($42.6\%$ to $<3\%$), and an automated skeleton-based pipeline converts optimized density fields into \rev{candidate geometry ready for computer-aided design. By retargeting the generative prior across domains, loading conditions, and physics objectives through a change of text prompt, with each new problem's physics setup specified separately, the framework uses a pretrained generative model as a reusable, training-free prior for engineering design.