IGG: Image Generation Informed by Geodesic Dynamics in Deformation Spaces

2025-04-09

AI Summary

Existing generative models lack explicit geometric modeling of anatomical structures, limiting their applicability in geometry-sensitive domains such as computational anatomy and biology. To address this, we propose the first image generation and editing framework grounded in geodesic dynamics on deformation manifolds: deformations are modeled as geodesic trajectories in latent space; an efficient geodesic autoencoder is designed; and a text-conditioned latent geodesic diffusion mechanism is introduced—ensuring topological preservation and geometric consistency while enabling semantic controllability. Differential-geometric constraints are incorporated into optimization to enhance deformation interpretability and structural fidelity. Evaluated on plant growth modeling and brain MRI data, our method surpasses state-of-the-art approaches, producing images with realistic texture, intact topology, and reduced artifacts, while supporting high-fidelity geometric editing.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Generative models have recently gained increasing attention in image generation and editing tasks. However, they often lack a direct connection to object geometry, which is crucial in sensitive domains such as computational anatomy, biology, and robotics. This paper presents a novel framework for Image Generation informed by Geodesic dynamics (IGG) in deformation spaces. Our IGG model comprises two key components: (i) an efficient autoencoder that explicitly learns the geodesic path of image transformations in the latent space; and (ii) a latent geodesic diffusion model that captures the distribution of latent representations of geodesic deformations conditioned on text instructions. By leveraging geodesic paths, our method ensures smooth, topology-preserving, and interpretable deformations, capturing complex variations in image structures while maintaining geometric consistency. We validate the proposed IGG on plant growth data and brain magnetic resonance imaging (MRI). Experimental results show that IGG outperforms the state-of-the-art image generation/editing models with superior performance in generating realistic, high-quality images with preserved object topology and reduced artifacts. Our code is publicly available at https://github.com/nellie689/IGG.

Problem

• Generating images with geometry-aware deformations for sensitive domains
• Learning geodesic paths in latent space for smooth image transformations
• Ensuring topology-preserving deformations in image generation and editing

Innovation

• Autoencoder learns geodesic image transformation paths
• Latent geodesic diffusion model captures deformation distributions
• Geodesic paths ensure smooth topology-preserving deformations