NeurIPS 2026
Flow-Corrected Shape Optimization: Taming Manifold Drift in High-Dimensional 3D Models
TL;DR Gradient-based optimization in the latent space of large 3D generative models drifts off the manifold of valid shapes. FCSO alternates free gradient steps on the objective with a flow-matching correction that brings the latent back onto the manifold: optimize freely, correct strictly.
Video
A 2.5-minute explainer of manifold drift and FCSO (with voice-over and captions).
Abstract
Optimizing 3D shapes within the latent spaces of deep generative models is fundamental to computer assisted engineering, yet remains prone to a critical failure mode we term manifold drift: the tendency of gradient-based optimization to move latent vectors away from the manifold of valid shapes. This problem is exacerbated in state-of-the-art 3D shape generative models that operate in increasingly high-dimensional latent spaces where valid shapes occupy a vanishingly small fraction of the full space. Existing mitigation strategies, including latent regularization and flow-matching approaches, either sacrifice expressiveness, demand a difficult trade-off between objective guidance and generative fidelity that remains prone to manifold drift, or are computationally infeasible to scale to modern, large-capacity 3D shape models. We introduce a novel optimizer-corrector framework that alternates between gradient steps for objective minimization and guided flow matching to drive the latent state back to the valid shape manifold. By decoupling objective minimization from flow-based correction, optimizing freely and correcting strictly, this alternating design avoids inherent trade-offs, preserving geometric validity without sacrificing expressiveness while remaining computationally feasible on modern 3D shape models. We demonstrate its effectiveness across generative priors of varying complexity, from simple vector latent spaces to large-scale architectures across a variety of downstream optimization tasks, including aerodynamic drag reduction and object compliance optimization.
Gradient descent vs. FCSO
Same starting shapes and same objective value reached: plain gradient descent breaks the shapes, FCSO keeps them valid.
Method
Modern 3D generative models decode a latent code into a shape. Valid shapes lie on a thin manifold of that latent space, and the manifold takes up a smaller and smaller share of the space as models get bigger. Plain gradient descent on an engineering objective ignores the manifold and drifts away from it. We call this manifold drift.
Existing fixes built on flow matching either do objective guidance and generation in a single pass, which forces a trade-off, or backpropagate through the whole flow, which does not scale to large models. FCSO gives each job its own step and repeats the following cycle:
- Optimize: take a few plain gradient steps on the objective.
- Correct: partially re-noise the latent, then let a pre-trained flow model carry it back onto the manifold, guided by the objective value reached in step 1.
Each cycle makes progress on the objective, then returns the latent to the manifold. FCSO works with generative priors ranging from simple vector latent spaces to large-scale models such as Hunyuan3D, on tasks such as aerodynamic drag reduction, volume reduction and compliance optimization.
Citation
@inproceedings{seiler2026fcso,
title = {Flow-Corrected Shape Optimization: Taming Manifold Drift in High-Dimensional 3D Models},
author = {Seiler, Emilien and Talabot, Nicolas and You, Yingxuan and Stella, Federico and Fua, Pascal},
booktitle = {Advances in Neural Information Processing Systems (NeurIPS)},
year = {2026}
}