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

We present an inference-time guidance framework for generating 3D multi-class anatomical voxel maps with localized geometric and topological control. During generation, we use cuboidal control domains of varying dimensionality, location, and shape to slice out relevant substructures. These local substructures are used to compute differentiable penalty functions that steer the sample towards target constraints. We penalize geometric features such as size, shape, position, and orientation through voxel-wise moments, while topological features such as connected components, loops, and voids are enforced through persistent homology. Lastly, we implement this guidance framework for latent diffusion models, where a neural field decoder can partially extract substructures, enabling efficient measurement and control of anatomical properties. 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 show that Anatomica flexibly applies to a variety of anatomical systems, enabling the rational design of synthetic datasets for virtual simulation trials or machine learning workflows.