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Coupled Geometry Distributions

MCML Authors

Riccardo Marin

Prof. Dr.

Core PI

Machine Learning for Robotics

Daniel Cremers

Prof. Dr.

Director

Computer Vision & Artificial Intelligence

Abstract

Existing 3D representations decouple geometry from correspondence: explicit representations tie correspondence to their discretization, while implicit ones require costly procedures to recover it. We introduce Coupled Geometry Distributions (CoGeDi), a continuous yet explicit representation modeling shape collections as a joint diffusion process over tuples of corresponding surface points. Building on Geometry Distributions, CoGeDi assigns each shape its own noise level, so that a single diffusion model supports both joint sampling across shapes and conditional correspondence prediction starting from a query point on one of the shapes. We further propose a sigma-clamping training strategy that improves conditional correspondence while preserving geometric fidelity. Experiments show that CoGeDi matches the geometric quality of independent per-shape models while accurately capturing joint and conditional relations across shapes. Finally, the representation naturally extends to additional attributes such as texture and time, enabling information transfer and synchronized animations.

inproceedings KMC26

GeoInt @ECCV 2026

Workshop on Geometric Intelligence: From Vision to Scientific Discovery at the 19th European Conference on Computer Vision. Malmö, Sweden, Sep 08-12, 2026.