Related papers: Flow Matching from Viewpoint of Proximal Operators
Continuous normalizing flows (CNFs) learn an ordinary differential equation to transform prior samples into data. Flow matching (FM) has recently emerged as a simulation-free approach for training CNFs by regressing a velocity model towards…
Over the past few years, numerous computational models have been developed to solve Optimal Transport (OT) in a stochastic setting, where distributions are represented by samples and where the goal is to find the closest map to the ground…
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…
Recent advances in cross-modal few-shot adaptation treat visual-semantic alignment as a continuous feature transport problem via Flow Matching (FM). However, we argue that Euclidean-based FM overlooks fundamental limitations of flat…
The DC Optimal Power Flow (DC-OPF) problem is fundamental to power system operations, requiring rapid solutions for real-time grid management. While traditional optimization solvers provide optimal solutions, their computational cost…
We present theoretical convergence guarantees for ODE-based generative models, specifically flow matching. We use a pre-trained autoencoder network to map high-dimensional original inputs to a low-dimensional latent space, where a…
Forecasting conditional stochastic nonlinear dynamical systems is a fundamental challenge repeatedly encountered across the biological and physical sciences. While flow-based models can impressively predict the temporal evolution of…
The Optimal Power Flow (OPF) problem is integral to the functioning of power systems, aiming to optimize generation dispatch while adhering to technical and operational constraints. These constraints are far from straightforward; they…
Optimal transport (OT) and Schr{\"o}dinger bridge (SB) problems have emerged as powerful frameworks for transferring probability distributions with minimal cost. However, existing approaches typically focus on endpoint matching while…
Flow matching trains a neural velocity field by regression against a target velocity associated with a prescribed probability path connecting a simple initial distribution to the data distribution. A central design choice is the path…
Forecasting high-dimensional, PDE-governed dynamics remains a core challenge for generative modeling. Existing autoregressive and diffusion-based approaches often suffer cumulative errors and discretisation artifacts that limit long,…
Optimal Transport (OT) is being widely used in various fields such as machine learning and computer vision, as it is a powerful tool for measuring the similarity between probability distributions and histograms. In previous studies, OT has…
Generative modelling has seen significant advances through simulation-free paradigms such as Flow Matching, and in particular, the MeanFlow framework, which replaces instantaneous velocity fields with average velocities to enable efficient…
Unbalanced optimal transport (UOT) provides a principled framework for modeling single-cell transitions and birth-death dynamics, but its high computational cost limits scalability to large-scale datasets. Although single-cell data often…
The AC Optimal Power Flow (AC-OPF) is a key building block in many power system applications. It determines generator setpoints at minimal cost that meet the power demands while satisfying the underlying physical and operational…
Flow models transform data gradually from one modality (e.g. noise) onto another (e.g. images). Such models are parameterized by a time-dependent velocity field, trained to fit segments connecting pairs of source and target points. When the…
Flow matching has recently emerged as a powerful framework for continuous-time generative modeling. However, when applied to long-tailed distributions, standard flow matching suffers from majority bias, producing minority modes with low…
Flow matching (FM) is a family of training algorithms for fitting continuous normalizing flows (CNFs). Conditional flow matching (CFM) exploits the fact that the marginal vector field of a CNF can be learned by fitting least-squares…
We introduce \emph{in-context operator learning on probability measure spaces} for optimal transport (OT). The goal is to learn a single solution operator that maps a pair of distributions to the OT map, using only few-shot samples from…
Controlled generation with pre-trained Diffusion and Flow Matching models has vast applications. One strategy for guiding ODE-based generative models is through optimizing a target loss $R(x_1)$ while staying close to the prior…