Anatomica: Localized Control over Geometric and Topological Properties for Anatomical Diffusion Models

摘要

Controllable generation of anatomical structures enables the rational design of synthetic datasets for virtual simulation trials and machine learning workflows. We present an inference-time guidance framework for generating 3D multi-class anatomical segmentations with localized geometric and topological control. During inference, we use cuboidal control domains of varying dimensionality, location, and extent to isolate relevant substructures and compute differentiable penalty functions that steer samples toward target constraints. We enforce geometric features such as size, shape, position, and orientation via voxel-wise moments, while topological features such as connected components, loops, and voids are enforced through persistent homology. Finally, we adapt this framework for latent diffusion models, where a neural field decoder can partially extract substructures, enabling efficient measurement and control of anatomical features. This formulation unlocks a rich design space where several constraints can be composed to control complex structures defined over arbitrary dimensions and coordinate systems. We release our code at https://github.com/kkadry/Anatomica.