Related papers: Discovering Data Manifold Geometry via Non-Contrac…
Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable…
This work presents DCFlow, a novel unsupervised cross-modal flow estimation framework that integrates a decoupled optimization strategy and a cross-modal consistency constraint. Unlike previous approaches that implicitly learn flow…
Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…
System identification has greatly benefited from deep learning techniques, particularly for modeling complex, nonlinear dynamical systems with partially unknown physics where traditional approaches may not be feasible. However, deep…
Data-driven reduced-order models of the dynamics of complex flows are important for tasks related to design, understanding, prediction, and control. Many flows obey symmetries, and the present work illustrates how these can be exploited to…
Vessel segmentation is an essential task in many clinical applications. Although supervised methods have achieved state-of-art performance, acquiring expert annotation is laborious and mostly limited for two-dimensional datasets with a…
We present a framework for learning probability distributions on topologically non-trivial manifolds, utilizing normalizing flows. Current methods focus on manifolds that are homeomorphic to Euclidean space, enforce strong structural priors…
We present ShapeFlow, a flow-based model for learning a deformation space for entire classes of 3D shapes with large intra-class variations. ShapeFlow allows learning a multi-template deformation space that is agnostic to shape topology,…
Considering smooth mappings from input vectors to continuous targets, our goal is to characterise subspaces of the input domain, which are invariant under such mappings. Thus, we want to characterise manifolds implicitly defined by level…
To model manifold data using normalizing flows, we employ isometric autoencoders to design embeddings with explicit inverses that do not distort the probability distribution. Using isometries separates manifold learning and density…
We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…
Flow matching models typically use linear interpolants to define the forward/noise addition process. This, together with the independent coupling between noise and target distributions, yields a vector field which is often non-straight.…
We present a novel deep learning framework for flow field predictions in irregular domains when the solution is a function of the geometry of either the domain or objects inside the domain. Grid vertices in a computational fluid dynamics…
We present a novel view of nonlinear manifold learning using derivative-free optimization techniques. Specifically, we propose an extension of the classical multi-dimensional scaling (MDS) method, where instead of performing gradient…
Real-world data with underlying structure, such as pictures of faces, are hypothesized to lie on a low-dimensional manifold. This manifold hypothesis has motivated state-of-the-art generative algorithms that learn low-dimensional data…
Disentangled representation learning aims to capture the underlying explanatory factors of observed data, enabling a principled understanding of the data-generating process. Recent advances in generative modeling have introduced new…
This paper concerns the problem of multi-object tracking based on the min-cost flow (MCF) formulation, which is conventionally studied as an instance of linear program. Given its computationally tractable inference, the success of MCF…
Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately, current approaches are only available for the most basic geometries and fall short when the underlying…
We introduce ContinualFlow, a principled framework for targeted unlearning in generative models via Flow Matching. Our method leverages an energy-based reweighting loss to softly subtract undesired regions of the data distribution without…
Flow matching models have emerged as a powerful method for generative modeling on domains like images or videos, and even on irregular or unstructured data like 3D point clouds or even protein structures. These models are commonly trained…