Related papers: Discovering Symmetry Groups with Flow Matching
Iterative generative models such as Flow Matching and Diffusion models have demonstrated strong test-time scaling behavior, where additional inference computation can improve generation quality. In contrast, Drift Models offer efficient…
We introduce an approach based on moving frames for polygon recognition and symmetry detection. We present detailed algorithms for recognition of polygons modulo the special Euclidean, Euclidean, equi-affine, skewed-affine and similarity…
Over the past decade, machine learning model complexity has grown at an extraordinary rate, as has the scale of the systems training such large models. However there is an alarmingly low hardware utilization (5-20%) in large scale AI…
Molecular structure elucidation is a fundamental step in understanding chemical phenomena, with applications in identifying molecules in natural products, lab syntheses, forensic samples, and the interstellar medium. We consider the task of…
Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models…
Symmetry is a fundamental concept that has been extensively studied, yet detecting it in complex scenes remains a significant challenge in computer vision. Recent heatmap-based approaches can localize potential regions of symmetry axes but…
Given datasets from multiple domains, a key challenge is to efficiently exploit these data sources for modeling a target domain. Variants of this problem have been studied in many contexts, such as cross-domain translation and domain…
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…
We propose Flow Mismatching, an unsupervised anomaly detection method that deliberately avoids reconstruction-based paradigms. Instead, we treat flow matching as geometric dynamics and leverage a key insight: anomalies occur at places where…
Learning disentangled representations is a key step towards effectively discovering and modelling the underlying structure of environments. In the natural sciences, physics has found great success by describing the universe in terms of…
Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and…
Flow matching as a paradigm of generative model achieves notable success across various domains. However, existing methods use either multi-round training or knowledge within minibatches, posing challenges in finding a favorable coupling…
Taming the generation outcome of state of the art Diffusion and Flow-Matching (FM) models without having to re-train a task-specific model unlocks a powerful tool for solving inverse problems, conditional generation, and controlled…
Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source distribution into a target distribution. Despite being a fundamental building block, conditional paths…
Diffusion and flow-based models have enabled significant progress in generation tasks across various modalities and have recently found applications in predictive learning. However, unlike typical generation tasks that encourage sample…
We study a nonlinear system of partial differential equations which describe rotating shallow water with an arbitrary constant polytropic index $\gamma $ for the fluid. In our analysis we apply the theory of symmetries for differential…
The task of reflection symmetry detection remains challenging due to significant variations and ambiguities of symmetry patterns in the wild. Furthermore, since the local regions are required to match in reflection for detecting a symmetry…
Learning-based planners leveraging Graph Neural Networks can learn search guidance applicable to large search spaces, yet their potential to address symmetries remains largely unexplored. In this paper, we introduce a graph representation…
Flow-matching models provide a powerful framework for various applications, offering efficient sampling and flexible probability path modeling. These models are characterized by flows with low curvature in learned generative trajectories,…
The Lie point symmetries and corresponding invariant solutions are obtained for a Gaussian, irrotational, compressible fluid flow. A supersymmetric extension of this model is then formulated through the use of a superspace and superfield…