发表机构
University of Virginia; Yale School of Medicine（弗吉尼亚大学; 耶鲁医学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对现有生成模型忽略几何拓扑一致性和形变不可解释的问题，提出IGG框架，将保持拓扑的测地线原理融入扩散生成过程，在测地线形变空间中合成多样样本，实现可解释且物理信息丰富的图像视频生成。
AI 中文摘要
生成扩散模型已成为各种成像应用（包括但不限于合成、重建和分割）的一类强大技术。尽管取得了成功，当前的生成模型存在两个关键局限性。首先，它们主要依赖图像强度和纹理信息，对底层对象几何形状的关注有限。因此，它们无法保证生成过程中的几何或拓扑一致性，而这对于计算解剖学、生物学和机器人等高风险领域至关重要，在这些领域中保持对象结构至关重要。其次，现有模型无法在生成过程中显式学习或表示形状变化。这种形变动态仍被遮蔽在网络参数中，使得变换过程不可解释且缺乏物理信息。为了解决这些挑战，我们引入了IGG（由测地线动态信息引导的图像生成），这是一种新颖的框架，将保持拓扑的测地线原理整合到基于扩散的生成过程中。与在图像强度空间中操作的传统方法相比，IGG在测地线形变空间中学习并合成多样化的样本，其中几何对象变化被学习为从给定模板/源图像到目标图像的平滑且可逆的光滑映射。我们的代码在此https URL上公开可用。
英文摘要
Generative diffusion models have emerged as a class of powerful techniques for various imaging applications, including but not limited to synthesis, reconstruction, and segmentation. Despite their success, current generative models pose two key limitations. First, they primarily rely on image intensity and texture information, with limited attention to underlying object geometry. As a result, they do not guarantee geometric or topological consistency during the generation process, which is a crucial requirement for high-stakes domains such as computational anatomy, biology, and robotics, where preserving object structure is critical. Second, existing models fail to explicitly learn or represent shape changes in the generative process. Such deformation dynamics remain occluded within network parameters; hence leaving the transformation process uninterpretable and physically uninformed. To address these challenges, we introduce IGG (Image Generation informed by Geodesic dynamics), a novel framework that integrates topology-preserving geodesic principles into the diffusion-based generative process. In contrast to conventional methods that operate in image intensity space, IGG learns and synthesizes diverse samples within geodesic deformation spaces, where geometric object changes are learned as smooth and invertible smooth mappings from a given template/source image. Our code is publicly available at https://github.com/nellie689/IGG.
