AI 中文总结
该研究针对高维3D形状生成模型优化中出现的流形漂移问题，提出优化器-校正器交替的流校正框架，在不牺牲表达能力的前提下实现有效校正，可用于多种3D形状优化任务。
AI 中文摘要
在深度生成模型的隐空间内优化3D形状是计算机辅助工程的基础，但仍易出现一种被称为流形漂移的关键失效模式：基于梯度的优化会使隐向量偏离有效形状的流形。在当前最先进的3D形状生成模型中，该问题会进一步加剧，这些模型在日益高维的隐空间中运行，而有效形状仅占据整个空间的极小部分。现有的缓解策略包括隐空间正则化和流匹配方法，要么牺牲表达能力，要么在目标引导与生成保真度之间进行难以权衡的取舍，仍易出现流形漂移，要么在计算上无法扩展到现代大容量3D形状模型。我们提出一种新颖的优化器-校正器框架，该框架交替执行目标最小化的梯度步骤和引导流匹配，以将隐态拉回有效形状流形。通过将目标最小化与基于流的校正解耦，实现自由优化与严格校正，这种交替设计避免了固有权衡，在不牺牲表达能力的前提下保持了几何有效性，同时对现代3D形状模型仍具有计算可行性。我们在不同复杂度的生成先验上验证了其有效性，从简单的向量隐空间到大规模架构，覆盖多种下游优化任务，包括空气动力学减阻和物体柔顺性优化。
英文摘要
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.
Comments31 pages, 16 figures
