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Compositional Generative Inverse Design
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Proposes CinDM, which casts inverse design as joint energy minimization over trajectories and boundaries using a diffusion model, and composes diffusion models over subsets of design variables to generalize to longer trajectories, more bodies, and more airfoils.
Problem
Inverse design of high-dimensional design parameters (initial states, boundary shapes) via learned dynamics models suffers from over-optimization into adversarial, out-of-distribution designs, and fails to generalize to more complex designs (longer horizons, more objects, more parts) than seen in tr
Approach
Optimize jointly over trajectory and boundary using the energy function implicitly defined by a diffusion model (rather than a surrogate forward model), and compose energy functions over overlapping subsets of design variables (time windows, body pairs, airfoil parts) at test time to generalize to more complex designs.
Key results
- On N-body 2-body 24-54 step designs, CinDM achieves the best MAE at 24, 34, 44 and 54 steps (e.g., 0.01264 vs 0.01974 for best baseline at 24 steps), averaging 15.8% MAE improvement.
- On 8-body 24-step designs, CinDM design objective 0.3062 vs 0.3251 for Backprop GNS, and MAE 0.09241 vs 0.15917.
- In 2-airfoil design, CinDM reaches lift-to-drag ratio 1.4216 vs best baseline ~1.0568, and discovers formation flying reducing drag by 53.6%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CinDM instead of Backprop with U-Net | 2-body inverse design · 2-body 24 steps | design obj: 0.1228 -> 0.1160 | Helped |
| Use CinDM instead of Backprop with U-Net | 2-body inverse design · 2-body 24 steps | MAE: 0.01974 -> 0.01264 | Helped |
| Use CinDM instead of Backprop with U-Net | 2-body inverse design · 2-body 34 steps | design obj: 0.1171 -> 0.1288 | Hurt |
| Use CinDM instead of Backprop with U-Net | 2-body inverse design · 2-body 34 steps | MAE: 0.01236 -> 0.00917 | Helped |
| Compose diffusion models over pairwise interactions to handle more bodies | CinDM · 4-body 24 steps | design obj: 0.2947 -> 0.2034 | Helped |
| Compose diffusion models over pairwise interactions to handle more bodies | CinDM · 4-body 24 steps | MAE: 0.09871 -> 0.03928 | Helped |
| Use compositional boundary modeling for multiple airfoils | CinDM · 2 airfoils | lift-to-drag ratio: 1.0914 -> 1.4216 | Helped |
| Use compositional boundary modeling for multiple airfoils | CinDM · 2 airfoils | design obj: 0.0891 -> 0.1986 | Hurt |
| Replace time composition with a single diffusion model over 44 steps (ablation) | CinDM · 2-body 44 steps | design_obj: 0.1326 ± 0.0087 -> 0.2779 ± 0.0197 | Hurt |
| Replace time composition with a single diffusion model over 44 steps (ablation) | CinDM · 4-body 44 steps | MAE: 0.03195 ± 0.00705 -> 0.05166 ± 0.01218 | Hurt |
Surprising findings
- The model discovers formation flying (leader-follower) in the 2-airfoil case that reduces drag by 53.6% versus separate flight.
- Directly diffusing 44 steps without time composition performs worse than the composed approach despite having about twice the parameters.
Limitations
- Design objective is sometimes weaker than the strongest baseline (e.g., Backprop U-Net at 34-54 steps and CEM/FNO-type baselines on single airfoil objective).
- Airfoil results show similar design objective to baselines; gains are mainly in lift-to-drag ratio, and the lambda hyperparameter is tuned by hand.
- Evaluation limited to simple synthetic 2D/N-body settings.
Experimental setup
Datasets: Pymunk-generated N-body trajectories Lily-Pad generated 2D fluid airfoil simulations
Benchmarks: N-body interaction (2-body 24-54 steps, 4-body, 8-body) 2D multi-airfoil design with Navier-Stokes (Lily-Pad)
Metrics: design objective MAE lift-to-drag ratio
Baselines: CEM Backprop GNS FNO LE-PDE
Builds on: classifier guidance reduce reuse recycle compositional diffusion Graph Network Simulator Backprop through learned surrogates
Closest papers by meaning
- 3DID: Direct 3D Inverse Design for Aerodynamics with Physics-Aware Optimization (NeurIPS 2025 · similarity 0.89)
- AFBench: A Large-scale Benchmark for Airfoil Design (NeurIPS 2024 · similarity 0.87)
- CcDPM: A Continuous Conditional Diffusion Probabilistic Model for Inverse Design (AAAI 2024 · similarity 0.84)
- Generative Adversarial Model-Based Optimization via Source Critic Regularization (NeurIPS 2024 · similarity 0.84)
- DecompDreamer: A Composition-Aware Curriculum for Structured 3D Asset Generation (NeurIPS 2026 · similarity 0.84)
- Improving Compositional Generation with Diffusion Models Using Lift Scores (ICML 2025 · similarity 0.84)
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