AMG: Adaptive Multi-point Guidance for Aerodynamic Design via Diffusion Models

Aerodynamic inverse design aims to find a wing geometry that achieves specified lift and drag coefficients across multiple flight conditions. Diffusion models have recently emerged as a promising tool for this task, but existing approaches coordinate multiple operating conditions through manually tuned or heuristic weighting schemes, which cannot adaptively resolve conflicts among targets. We propose Adaptive Multi-point Guidance (AMG), an inference-time guidance framework that steers a pretrained diffusion model by solving a linear system in the latent space. At each denoising step, AMG evaluates the denoised prediction with a differentiable surrogate model, constructs the physical Jacobian of the aerodynamic coefficients with respect to the latent variable, and solves for a latent displacement whose pseudo-inverse solution automatically determines the contribution of each target. This formulation replaces the noise-space scalar weighting of classifier guidance with a latent-space vector displacement, and enables adaptive coordination of competing aerodynamic objectives without manual weight tuning. On a set of multi-point design tasks constructed from the SuperWing dataset, AMG reduces the average MAPE by 69% relative to the best-performing baseline among those considered in this work, where the MAPE is evaluated by the same surrogate model used for guidance and reported at the best intermediate step of sampling. These results suggest that AMG has the potential to be applied in practical aerodynamic design.