# Geodesic-informed Generative Diffusion Model For Topology-preserved Image Video Generation

arXiv: https://arxiv.org/abs/2609.08153 · HTML: https://mlsanity.com/paper/2609.08153/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 40 of its 66 references that are in the map.
- First posted on arXiv 8 Sep 2026.

## Placed in

- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

## Builds on (most cited first, 30 of 40)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [InstructPix2Pix: Learning to Follow Image Editing Instructions](https://mlsanity.com/paper/2211.09800/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [CogVideoX: Text-to-Video Diffusion Models with An Expert Transformer](https://mlsanity.com/paper/2408.06072/) (2024)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [Towards Accurate Generative Models of Video: A New Metric & Challenges](https://mlsanity.com/paper/1812.01717/) (2018)
- [Imagic: Text-Based Real Image Editing with Diffusion Models](https://mlsanity.com/paper/2210.09276/) (2022)
- [DynamiCrafter: Animating Open-domain Images with Video Diffusion Priors](https://mlsanity.com/paper/2310.12190/) (2023)
- [BLIP-Diffusion: Pre-trained Subject Representation for Controllable Text-to-Image Generation and Editing](https://mlsanity.com/paper/2305.14720/) (2023)
- [Unsupervised Medical Image Translation with Adversarial Diffusion Models](https://mlsanity.com/paper/2207.08208/) (2022)
- [Localizing Object-level Shape Variations with Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.11306/) (2023)
- [Diffusion Models Beat GANs on Topology Optimization](https://mlsanity.com/paper/2208.09591/) (2022)
- [DiffuseMorph: Unsupervised Deformable Image Registration Using Diffusion Model](https://mlsanity.com/paper/2112.05149/) (2021)
- [SADM: Sequence-Aware Diffusion Model for Longitudinal Medical Image Generation](https://mlsanity.com/paper/2212.08228/) (2022)
- [Unsupervised Domain Adaptation via Disentangled Representations: Application to Cross-Modality Liver Segmentation](https://mlsanity.com/paper/1907.13590/) (2019)
- [MR image reconstruction using deep density priors](https://mlsanity.com/paper/1711.11386/) (2017)
- [MGGAN: Solving Mode Collapse using Manifold Guided Training](https://mlsanity.com/paper/1804.04391/) (2018)
- [A Structural Causal Model for MR Images of Multiple Sclerosis](https://mlsanity.com/paper/2103.03158/) (2021)
- [Generative Self-training for Cross-domain Unsupervised Tagged-to-Cine MRI Synthesis](https://mlsanity.com/paper/2106.12499/) (2021)
- [Topology-Aware Latent Diffusion for 3D Shape Generation](https://mlsanity.com/paper/2401.17603/) (2024)
- [SADIR: Shape-Aware Diffusion Models for 3D Image Reconstruction](https://mlsanity.com/paper/2309.03335/) (2023)
- [TopoDiffusionNet: A Topology-aware Diffusion Model](https://mlsanity.com/paper/2410.16646/) (2024)
- [NeurEPDiff: Neural Operators to Predict Geodesics in Deformation Spaces](https://mlsanity.com/paper/2303.07115/) (2023)

## Abstract (arXiv)

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.