Related papers: Geometry-Aware Image Flow Matching
Recovering the camera motion and scene geometry from visual data is a fundamental problem in the field of computer vision. Its success in standard vision is attributed to the maturity of feature extraction, data association and multi-view…
Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
This paper presents a groundbreaking approach to causal inference by integrating continuous normalizing flows (CNFs) with parametric submodels, enhancing their geometric sensitivity and improving upon traditional Targeted Maximum Likelihood…
The study of diffeomorphism groups and their applications to problems in analysis and geometry has a long history. In geometric hydrodynamics, pioneered by V.~Arnold in the 1960s, one considers an ideal fluid flow as the geodesic motion on…
Flow-based Generative Models (FGMs) effectively transform noise into complex data distributions. Incorporating Optimal Transport (OT) to couple noise and data during FGM training has been shown to improve the straightness of flow…
This paper introduces the sigma flow model for the prediction of structured labelings of data observed on Riemannian manifolds, including Euclidean image domains as special case. The approach combines the Laplace-Beltrami framework for…
Stochastic geometric mechanics (SGM) is known for its potential utility in quantifying uncertainty in global climate modelling of the Earth's ocean and atmosphere while also preserving the fundamental advective transport properties of ideal…
Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that…
Accurate inference of fine-grained traffic flow from coarse-grained one is an emerging yet crucial problem, which can help greatly reduce the number of the required traffic monitoring sensors for cost savings. In this work, we notice that…
In this paper, we focus on designing effective method for fast and accurate scene parsing. A common practice to improve the performance is to attain high resolution feature maps with strong semantic representation. Two strategies are widely…
Flow Matching is a powerful framework for learning transport maps between probability distributions. Yet its standard single-parameter formulation is not designed to capture multi-parameter variations where the resulting transport should be…
The optimal transport (OT) problem aims to find the most efficient mapping between two probability distributions under a given cost function, and has diverse applications in many fields such as machine learning, computer vision and computer…
Diffusion and flow models have become the dominant paradigm for generative modeling on Riemannian manifolds, with successful applications in protein backbone generation and DNA sequence design. However, these methods require tens to…
Enhancing the efficiency of high-quality image generation using Diffusion Models (DMs) is a significant challenge due to the iterative nature of the process. Flow Matching (FM) is emerging as a powerful generative modeling paradigm based on…
Medical image segmentation plays an important role in accurately identifying and isolating regions of interest within medical images. Generative approaches are particularly effective in modeling the statistical properties of segmentation…
Understanding and predicting object motion from egocentric video is fundamental to embodied perception and interaction. However, generating physically consistent 6DoF trajectories remains challenging due to occlusions, fast motion, and the…
Recent approaches on visual scene understanding attempt to build a scene graph -- a computational representation of objects and their pairwise relationships. Such rich semantic representation is very appealing, yet difficult to obtain from…
Recently, studies on machine learning have focused on methods that use symmetry implicit in a specific manifold as an inductive bias. Grassmann manifolds provide the ability to handle fundamental shapes represented as shape spaces, enabling…
Geometric navigation is nowadays a well-established field of robotics and the research focus is shifting towards higher-level scene understanding, such as Semantic Mapping. When a robot needs to interact with its environment, it must be…