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.
Existing 3D generative models predominantly rely on implicit volumetric representations, which enforce watertight topology and struggle to represent thin-shell and non-manifold geometries such as garments. Geometry image-based approaches offer a surface-centric alternative, but existing methods rely on discrete binary occupancy maps whose resolution-dependent boundary encoding causes staircase artifacts and information loss upon downsampling, while surface reconstruction remains a non-differentiable post-processing step disconnected from the learning pipeline. To address this, we propose Differentiable Geometry Image (DiffGI), an end-to-end 3D-to-2D mapping framework that seamlessly integrates surface representation and geometric optimization. DiffGI replaces binary maps with a continuous 2D Truncated Signed Distance Function (TSDF), which encodes boundary position at subpixel precision within a fixed grid resolution, eliminating resolution-dependent staircase artifacts even under aggressive downsampling. Building on this continuous field, we introduce a differentiable Marching Squares algorithm based on analytical linear interpolation, allowing gradients from 3D surface losses to propagate back to the 2D latent space. Leveraging this differentiable pipeline, we train a DiffGI-VAE augmented with a geometry-aware normal rendering loss to compress complex 3D surfaces into an ultra-compact 32X32 latent space, and instantiate a transformer-based latent diffusion model with a flow-matching objective on top of this space for conditional 3D generation. Extensive experiments on garment and object datasets demonstrate that our method achieves superior reconstruction fidelity and boundary precision compared to prior geometry-image and voxel-based approaches, while requiring significantly fewer computational resources.
Large-scale video diffusion models often fail to preserve 3D structure over time, causing geometric drift and implausible motion under viewpoint changes. Existing methods usually enforce geometric consistency by using explicit geometry reconstructions, such as depth maps, point clouds, or reconstructed 3D structures, to define conditions, supervision, or reward signals, making the generator sensitive to errors from upstream geometry pipelines. We propose VideoWeave, a latent-space post-training framework that uses implicit geometry-model features to constrain the generative distribution, providing a more flexible and non-rigid form of guidance that mitigates the impact of reconstruction errors from geometry models. Specifically, VideoWeave adapts these features into geometry latents and jointly models them with video latents in a shared denoising space, allowing geometry to shape the generative distribution during training. To support this process, we build GeoVid-80K, an 80K-video dataset with paired appearance and geometry representations. Experiments on text-to-video and image-to-video generation show that VideoWeave improves geometric coherence while preserving strong visual quality. VideoWeave project page at https://videoweave.github.io/
We introduce GeCo, a geometry-grounded metric for jointly detecting geometric deformation and occlusion-inconsistency artifacts in static scenes. By fusing residual motion and depth priors, GeCo produces interpretable, dense consistency maps that reveal these artifacts. We use GeCo to systematically benchmark recent video generation models, uncovering common failure modes, and further employ it as a training-free guidance loss to reduce deformation artifacts during video generation.