Related papers: Implicit geometric regularization in flow matching…
Overparameterized models may have many interpolating solutions; implicit regularization refers to the hidden preference of a particular optimization method towards a certain interpolating solution among the many. A by now established line…
The Wasserstein-Fisher-Rao (WFR) metric extends dynamic optimal transport (OT) by coupling displacement with change of mass, providing a principled geometry for modeling unbalanced snapshot dynamics. Existing WFR solvers, however, are often…
In this work, we consider the problem of training a generator from evaluations of energy functions or unnormalized densities. This is a fundamental problem in probabilistic inference, which is crucial for scientific applications such as…
Image segmentation is a complex mathematical problem, especially for images that contain intensity inhomogeneity and tightly packed objects with missing boundaries in between. For instance, Magnetic Resonance (MR) muscle images often…
Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (OFM) for learning stochastic process priors on function spaces. OFM…
Modeling complex systems that evolve toward equilibrium distributions is important in various physical applications, including molecular dynamics and robotic control. These systems often follow the stochastic gradient descent of an…
Weak gravitational lensing maps compactly encode the evolution of cosmic large-scale structure and are a key tool for cosmological analyses. Performing inference directly at the map level allows flexible choices of statistics and can…
Flow models have rapidly become the go-to method for training and deploying large-scale generators, owing their success to inference-time flexibility via adjustable integration steps. A crucial ingredient in flow training is the choice of…
Flow Matching (FM) (also referred to as stochastic interpolants or rectified flows) stands out as a class of generative models that aims to bridge in finite time the target distribution $\nu^\star$ with an auxiliary distribution $\mu$,…
Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different…
Flow matching (FM) constructs continuous-time ODE samplers by prescribing probability paths between a base distribution and a target distribution. In this note, we study FM through the lens of finite-sample plug-in estimation. In addition…
Recent progress in large-scale flow and diffusion models raised two fundamental algorithmic challenges: (i) control-based reward adaptation of pre-trained flows, and (ii) integration of multiple models, i.e., flow merging. While current…
Flow matching models have shown great potential in image generation tasks among probabilistic generative models. However, most flow matching models in the literature do not explicitly utilize the underlying clustering structure in the…
Functional data, i.e., smooth random functions observed over a continuous domain, are increasingly available in areas such as biomedical research, health informatics, and epidemiology. However, effective statistical analysis for functional…
Gromov-Wasserstein (GW) is a powerful tool to compare probability measures whose supports are in different metric spaces. GW suffers however from a computational drawback since it requires to solve a complex non-convex quadratic program. We…
Recent flow matching (FM) methods improve the few-shot adaptation of vision-language models, by modeling cross-modal alignment as a continuous multi-step flow. In this paper, we argue that existing FM methods are inherently constrained by…
Accurate emulation of multi-scale physical systems governed by PDEs demands models that remain stable over long autoregressive rollouts while preserving fine-scale structures. Deterministic emulators produce overly-smoothed predictions,…
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…
Generative models have achieved remarkable progress with the emergence of flow matching (FM). It has demonstrated strong generative capabilities and attracted significant attention as a simulation-free flow-based framework capable of…
Deep generative models often face a fundamental tradeoff: high sample quality can come at the cost of memorisation, where the model reproduces training data rather than generalising across the underlying data geometry. We introduce Carr\'e…