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Flow-Corrected Shape Optimization: Taming Manifold Drift in High-Dimensional 3D Models
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Proposes Flow-Corrected Shape Optimization (FCSO), alternating gradient descent on a shape latent with guided flow-matching correction to keep optimized 3D shapes on the valid manifold, evaluated on chair volume, car drag, and Hunyuan3D compliance tasks.
Problem
Gradient-based latent optimization of 3D shapes drifts off the manifold of valid shapes ("manifold drift"), producing degenerate shapes that exploit surrogate objectives; the problem worsens with high-dimensional latent spaces of modern 3D generators.
Approach
Decouple objective minimization from manifold correction: take M gradient steps on the latent, then partially noise the result (SDEdit-style) and integrate a pre-trained flow matching ODE guided by the objective value reached in the gradient phase, repeating for K cycles.
Key results
- On chair volume (3DShape2VecSet) at 70% reduction, FCSO achieves FD_incep 31.76 vs 32.73 for SGO and 88.12 for GD, and the best scores on all six metrics.
- On car drag (3DShape2VecSet) at 30% drag reduction, FCSO reaches FD_incep 89.08 vs 100.20 for FMG and 132.82 for GD.
- On Hunyuan3D compliance optimization of ABO tables, FCSO reaches FD_incep 49.97 vs 55.56 for SGO; D-Flow runs out of memory.
Surprising findings
- On the simpler DeepSDF prior, FCSO performs on par with baselines and brings no particular benefit.
- The SGO baseline is competitive on chair volume with 3DShape2VecSet but falls behind on the car drag and Hunyuan3D tasks.
Limitations
- Each optimization cycle needs N extra vector-field evaluations, making it slower than plain gradient descent.
- Under aggressive targets the method can introduce minor geometric artifacts.
- Hyperparameters M (gradient steps) and tau (noise ratio) are fixed rather than adaptive.
Experimental setup
Datasets: ShapeNet chairs ShapeNet cars ABO DrivAer-style OpenFOAM simulations
Benchmarks: chair volume reduction (ShapeNet) car drag optimization (ShapeNet) compliance optimization on ABO tables and chairs
Metrics: FD_incep KD_incep FD_dino KD_dino FD_point KD_point volume reduction drag coefficient compliance
Baselines: Gradient Descent Flow Matching Guidance D-Flow ICTM SGO
Builds on: flow matching rectified flow classifier-free guidance SDEdit D-Flow 3DShape2VecSet DeepSDF Score Guided Optimization
Closest papers by meaning
- GPLD3D: Latent Diffusion of 3D Shape Generative Models by Enforcing Geometric and Physical Priors (CVPR 2024 · similarity 0.90)
- Enhancing Implicit Shape Generators Using Topological Regularizations (ICML 2024 · similarity 0.88)
- Categorical Flow Matching on Statistical Manifolds (NeurIPS 2024 · similarity 0.87)
- ShapeShifter: 3D Variations Using Multiscale and Sparse Point-Voxel Diffusion (CVPR 2025 · similarity 0.87)
- Flow Matching on General Geometries (ICLR 2024 · similarity 0.87)
- PartCrafter: Structured 3D Mesh Generation via Compositional Latent Diffusion Transformers (NeurIPS 2025 · similarity 0.87)
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