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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. 

Abstract Stars primarily form in galactic spiral arms within dense, filamentary molecular clouds. The largest and most elongated of these molecular clouds are referred to as “bones,” which are massive, velocity-coherent filaments (lengths ∼20 to >100 pc, widths ∼1–2 pc) that run approximately parallel and in close proximity to the Galactic plane. While these bones have been generally well characterized, the importance and structure of their magnetic fields (B-fields) remain largely unconstrained. Through the Stratospheric Observatory for Infrared Astronomy Legacy program FIlaments Extremely Long and Dark: a Magnetic Polarization Survey (FIELDMAPS), we mapped the B-fields of 10 bones in the Milky Way. We found that their B-fields are varied, with no single preferred alignment along the entire spine of the bones. At higher column densities, the spines of the bones are more likely to align perpendicularly to the B-fields, although this is not ubiquitous, and the alignment shows no strong correlation with the locations of identified young stellar objects. We estimated the B-field strengths across the bones and found them to be ∼30–150μG at parsec scales. Despite the generally low virial parameters, the B-fields are strong compared to the local gravity, suggesting that B-fields play a significant role in resisting global collapse. Moreover, the B-fields may slow and guide gas flow during dissipation. Recent star formation within the bones may be due to high-density pockets at smaller scales, which could have formed before or simultaneously with the bones.