Related papers: Discovering Symmetry Groups with Flow Matching

Optical flow estimation is a challenging problem remaining unsolved. Recent deep learning based optical flow models have achieved considerable success. However, these models often train networks from the scratch on standard optical flow…

Flow Matching has recently emerged as a popular class of generative models for simulating a target distribution $\mu_1$ from samples drawn from a source distribution $\mu_0$. This framework relies on a fixed coupling between $\mu_0$ and…

Data heterogeneity hinders clinical deployment of medical image analysis models, and generative data augmentation helps mitigate this issue. However, recent diffusion-based methods that synthesize image-mask pairs often ignore distribution…

This work presents a general geometric framework for simulating and learning the dynamics of Hamiltonian systems that are invariant under a Lie group of transformations. This means that a group of symmetries is known to act on the system…

Object pose estimation is a fundamental problem in robotics and computer vision, yet it remains challenging due to partial observability, occlusions, and object symmetries, which inevitably lead to pose ambiguity and multiple hypotheses…

Generating high-quality time series data has emerged as a critical research topic due to its broad utility in supporting downstream time series mining tasks. A major challenge lies in modeling the intrinsic stochasticity of temporal…

We introduce ImitationFlow, a novel Deep generative model that allows learning complex globally stable, stochastic, nonlinear dynamics. Our approach extends the Normalizing Flows framework to learn stable Stochastic Differential Equations.…

Bayesian filtering and smoothing for high-dimensional nonlinear dynamical systems are fundamental yet challenging problems in many areas of science and engineering. In this work, we propose FLUID, a flow-based unified amortized inference…

Group equivariance can overly constrain models if the symmetries in the group differ from those observed in data. While common methods address this by determining the appropriate level of symmetry at the dataset level, they are limited to…

Traditional discriminative computer vision relies predominantly on static projections, mapping input features to outputs in a single computational step. Although efficient, this paradigm lacks the iterative refinement and robustness…

Generative modeling of physical systems, such as molecules, requires learning distributions that are invariant under global symmetries, such as rotations in three-dimensional space. Equivariant diffusion and flow matching models can…

We tackle the problem of estimating flow between two images with large lighting variations. Recent learning-based flow estimation frameworks have shown remarkable performance on image pairs with small displacement and constant…

The multi-step denoising process in diffusion and Flow Matching models causes major efficiency issues, which motivates research on few-step generation. We present Solution Flow Models (SoFlow), a framework for one-step generation from…

Finding and describing sub-populations that are exceptional regarding a target property has important applications in many scientific disciplines, from identifying disadvantaged demographic groups in census data to finding conductive…

Deep generative models that produce novel molecular structures have the potential to facilitate chemical discovery. Flow matching is a recently proposed generative modeling framework that has achieved impressive performance on a variety of…

In this work, Lie symmetry analysis is performed on a coupled nonlinear cross-diffusion system with varying cross-section geometry. The system describes two interacting quantities whose material properties, namely the capacity functions and…

We propose a modular, data-driven framework for jointly learning unknown functional mappings and discovering the underlying one-parameter symmetry subgroup governing the data. Unlike conventional geometric deep learning methods that assume…

Discovering symbolic differential equations from data uncovers fundamental dynamical laws underlying complex systems. However, existing methods often struggle with the vast search space of equations and may produce equations that violate…

We study the problem of self-supervised 3D scene flow estimation from real large-scale raw point cloud sequences, which is crucial to various tasks like trajectory prediction or instance segmentation. In the absence of ground truth scene…

Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to…