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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. 

This paper presents a multimodal deep learning framework that utilizes advanced image techniques to improve the performance of clinical analysis heavily dependent on routinely acquired standard images. More specifically, we develop a joint learning network that for the first time leverages the accuracy and reproducibility of myocardial strains obtained from Displacement Encoding with Stimulated Echo (DENSE) to guide the analysis of cine cardiac magnetic resonance (CMR) imaging in late mechanical activation (LMA) detection. An image registration network is utilized to acquire the knowledge of cardiac motions, an important feature estimator of strain values, from standard cine CMRs. Our framework consists of two major components: (i) a DENSE-supervised strain network leveraging latent motion features learned from a registration network to predict myocardial strains; and (ii) a LMA network taking advantage of the predicted strain for effective LMA detection. Experimental results show that our proposed work substantially improves the performance of strain analysis and LMA detection from cine CMR images, aligning more closely with the achievements of DENSE.