Geodesic Flow Matching on a Riemannian Degradation Manifold for Blind Image Restoration

Blind image restoration requires recovering clean images from observations corrupted by unknown and potentially mixed degradations. While recent deterministic flow-based methods model restoration as transport processes that map degraded images to clean ones, they typically rely on Euclidean interpolation, implicitly assuming linear degradation geometry. In this paper, we explicitly model degradations as points on a low-dimensional Riemannian manifold and formulate restoration as geodesic transport on the joint image-manifold space. Using a geodesic flow matching objective, we learn intrinsic transport dynamics that respect the curvature of degradation space. This framework generalizes linear flow matching, provides a principled treatment of mixed degradations as geodesic compositions, and yields a clean theoretical interpretation for generalization beyond observed degradations.

MoRAG -- Multi-Fusion Retrieval Augmented Generation for Human Motion

We introduce MoRAG, a novel multi-part fusion based retrieval-augmented generation strategy for text-based human motion generation. The method enhances motion diffusion models by leveraging additional knowledge obtained through an improved motion retrieval process. By effectively prompting large language models (LLMs), we address spelling errors and rephrasing issues in motion retrieval. Our approach utilizes a multi-part retrieval strategy to improve the generalizability of motion retrieval across the language space. We create diverse samples through the spatial composition of the retrieved motions. Furthermore, by utilizing low-level, part-specific motion information, we can construct motion samples for unseen text descriptions. Our experiments demonstrate that our framework can serve as a plug-and-play module, improving the performance of motion diffusion models. Code, pretrained models and sample videos will be made available at: https://motion-rag.github.io/