Related papers: Generalised Flow Maps for Few-Step Generative Mode…

Graph Foundation Models (GFMs) are emerging as a significant research topic in the graph domain, aiming to develop graph models trained on extensive and diverse data to enhance their applicability across various tasks and domains.…

Wasserstein gradient flows (WGFs) describe the evolution of probability distributions in Wasserstein space as steepest descent dynamics for a free energy functional. Computing the full path from an arbitrary initial distribution to…

Controlling generative models is computationally expensive. This is because optimal alignment with a reward function--whether via inference-time steering or fine-tuning--requires estimating the value function. This task demands access to…

We introduce Categorical Flow Maps, a flow-matching method for accelerated few-step generation of categorical data via self-distillation. Building on recent variational formulations of flow matching and the broader trend towards accelerated…

Many measurements or observations in computer vision and machine learning manifest as non-Euclidean data. While recent proposals (like spherical CNN) have extended a number of deep neural network architectures to manifold-valued data, and…

Numerous biological and physical processes can be modeled as systems of interacting entities evolving continuously over time, e.g. the dynamics of communicating cells or physical particles. Learning the dynamics of such systems is essential…

We present Functional Mean Flow (FMF) as a one-step generative model defined in infinite-dimensional Hilbert space. FMF extends the one-step Mean Flow framework to functional domains by providing a theoretical formulation for Functional…

Rapid and accurate simulations of fluid dynamics around complicated geometric bodies are critical in a variety of engineering and scientific applications, including aerodynamics and biomedical flows. However, while scientific machine…

We propose a novel Particle Flow Map (PFM) method to enable accurate long-range advection for incompressible fluid simulation. The foundation of our method is the observation that a particle trajectory generated in a forward simulation…

Modern generative models can produce realistic samples, however, balancing memorisation and generalisation remains an open problem. We approach this challenge from a Bayesian perspective by focusing on the parameter space of flow matching…

Data-driven Riemannian geometry has emerged as a powerful tool for interpretable representation learning, offering improved efficiency in downstream tasks. Moving forward, it is crucial to balance cheap manifold mappings with efficient…

Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…

The scarcity of labeled data is a long-standing challenge for many machine learning tasks. We propose our gradient flow method to leverage the existing dataset (i.e., source) to generate new samples that are close to the dataset of interest…

Realistic human geometry generation is an important yet challenging task, requiring both the preservation of fine clothing details and the accurate modeling of clothing-body interactions. To tackle this challenge, we build upon Geometry…

Generative modeling over discrete data has recently seen numerous success stories, with applications spanning language modeling, biological sequence design, and graph-structured molecular data. The predominant generative modeling paradigm…

What is the shortest path between two data points lying in a high-dimensional space? While the answer is trivial in Euclidean geometry, it becomes significantly more complex when the data lies on a curved manifold -- requiring a Riemannian…

This paper presents a novel paradigm in simulation-based engineering sciences by introducing a new framework called Generative Parametric Design (GPD). The GPD framework enables the generation of new designs along with their corresponding…

Flow maps enable high-quality image generation in a single forward pass. However, unlike iterative diffusion models, their lack of an explicit sampling trajectory impedes incorporating external constraints for conditional generation and…

Accurately modeling and predicting complex dynamical systems, particularly those involving force exchange and dissipation, is crucial for applications ranging from fluid dynamics to robotics, but presents significant challenges due to the…

An increasingly common viewpoint is that protein dynamics data sets reside in a non-linear subspace of low conformational energy. Ideal data analysis tools for such data sets should therefore account for such non-linear geometry. The…