RePaint-Enhanced Conditional Diffusion Model for Parametric Engineering Designs under Performance and Parameter Constraints

This paper presents a RePaint-enhanced framework that integrates a pre-trained performance-guided denoising diffusion probabilistic model (DDPM) for performance- and parameter-constraint engineering design generation. The proposed method enables the generation of missing design components based on a partial reference design while satisfying performance constraints, without retraining the underlying model. By applying mask-based resampling during inference process, RePaint allows efficient and controllable repainting of partial designs under both performance and parameter constraints, which is not supported by conventional DDPM-base methods. The framework is evaluated on two representative design problems, parametric ship hull design and airfoil design, demonstrating its ability to generate novel designs with expected performance based on a partial reference design. Results show that the method achieves accuracy comparable to or better than pre-trained models while enabling controlled novelty through fixing partial designs. Overall, the proposed approach provides an efficient, training-free solution for parameter-constraint-aware generative design in engineering applications.

💡 Research Summary

The paper introduces a novel framework that combines a pre‑trained performance‑guided denoising diffusion probabilistic model (DDPM) with the RePaint conditioning mechanism to enable generation of parametric engineering designs that satisfy both performance targets and parameter constraints, without any additional model retraining. Traditional conditional DDPMs can incorporate performance metrics as generation conditions, but they require retraining when new constraints or partial design inputs are introduced. RePaint overcomes this limitation by using a mask‑based resampling strategy during inference: known regions of a design are kept fixed, noise is added to match the diffusion step’s noise level, and unknown regions are iteratively “painted” using samples generated by the underlying DDPM. This iterative process reduces discontinuities at mask boundaries and allows arbitrary partial designs to be completed while respecting constraints.

The methodology proceeds as follows: (1) a performance‑guided DDPM is first trained on a full dataset (e.g., ship hulls or airfoils) with a performance conditioning module that predicts the difference between the current design’s performance and a target value. (2) During inference, the user supplies a target performance and a binary mask indicating which design parameters are fixed. (3) At a chosen diffusion timestep, the known parameters are perturbed with Gaussian noise to align their noise level with the unknown part. (4) The unknown part is sampled from the DDPM, combined with the noisy known part, and the reverse diffusion step is applied. (5) Steps 3‑4 are repeated multiple times per timestep, effectively “re‑painting” the missing region while preserving the fixed parameters.

Two case studies validate the approach. The first uses the Ship‑D dataset, containing 82,168 hull designs described by 45 geometric parameters and subject to 49 algebraic feasibility constraints. The target performance is the resistance coefficient. By fixing subsets of parameters (e.g., overall length, beam) and applying RePaint‑cDDPM, the remaining parameters are generated such that the final hull meets the resistance target and all feasibility constraints. The second case employs the UIUC airfoil dataset, where each airfoil is represented by ordered surface coordinates and the lift‑to‑drag ratio serves as the performance condition. Again, partial coordinate sets are fixed and the missing sections are completed by the RePaint‑enhanced model.

Results show that the RePaint‑cDDPM achieves performance errors within 2‑3 % of the target, comparable or superior to the baseline DDPM that was trained directly for the same task. Constraint violation rates remain below 1 %, demonstrating that the mask‑based inference respects the underlying algebraic constraints without retraining. Moreover, by varying the mask size and location, the authors demonstrate controllable novelty: larger masked regions yield more diverse designs, while smaller masks preserve more of the original geometry. This controllability is valuable for design exploration, allowing engineers to anchor certain critical dimensions while freely exploring the remaining design space.

The primary drawback identified is inference speed. RePaint requires multiple resampling iterations per diffusion step, making it slower than GAN‑based generators. The authors mitigate this by selecting a limited set of diffusion timesteps and reducing the number of RePaint iterations, but real‑time applications would still benefit from further optimization (e.g., parallelized noise addition, lightweight diffusion backbones). Additionally, the current implementation focuses on single‑objective performance conditioning; extending the framework to multi‑objective or hierarchical constraints would necessitate more sophisticated guidance networks.

In summary, the paper presents a training‑free, mask‑driven conditioning technique that extends the flexibility of conditional diffusion models for parametric engineering design. By integrating RePaint, the framework enables rapid adaptation to new performance targets, arbitrary partial designs, and parameter constraints without retraining the underlying generative model. This contribution opens pathways for more interactive, constraint‑aware generative design tools in fields such as naval architecture, aerodynamics, and beyond.