Existing optimal transport (OT) models primarily seek an OT map or plan between distributions by minimizing a prescribed transport cost or distortion. However, minimizing transport cost or distortion alone may fail to identify a geometrically meaningful transformation between the two distributions.
arXiv:2608. 19783v1 Announce Type: new Abstract: Existing optimal transport (OT) models primarily seek an OT map or plan between distributions by minimizing a prescribed transport cost or distortion.
arXiv:2608. 16506v1 Announce Type: cross Abstract: Dataset alignment is a central step in data analysis across science and engineering, where the goal is to match observations between datasets.
arXiv:2606. 04092v1 Announce Type: cross Abstract: Flow matching models learn to transport samples from a simple prior distribution to a complex data distribution.
Many modern generative modeling methods, including diffusion models, normalizing flows, and flow matching, estimate transport maps or plans between distributions without explicitly targeting an optimal transport (OT) map. In applications like generative modeling, the transport cost itself is irrelevant, and this makes it natural to target maps which are more tractable from either a statistical or computational standpoint.
arXiv:2608. 01692v1 Announce Type: new Abstract: We propose an instantiation of flow matching that relies on a time-independent velocity field (an \emph{autonomous flow}) to exactly map between two distributions, so long as the target is singular, i.
BridgeMatch is a two‑stage generative solver that preserves the full soft matching matrix for 3D deformable registration. Stage I uses denoising diffusion to estimate a global matching matrix at a coarse resolution, then lifts it to high resolution while maintaining hierarchy and rank constraints. Stage II refines this lifted matrix via a conditional transport bridge, implemented with either a deterministic Flow Matching ODE or a stochastic Brownian‑bridge SDE, and demonstrates improved correspondence accuracy and registration performance on 4DMatch, 4DLoMatch, CAPE, and DeepDeform datasets, especially in low‑overlap scenarios.
arXiv:2609.40075v1 Announce Type: new Abstract: Partial Optimal Transport (POT) extends the classical optimal transport problem by relaxing the strict mass conservation constraint, enabling its use i...
The paper introduces LA-VDM, a landmark‑constrained algorithm that speeds up Vector Diffusion Maps (VDM) by employing a two‑stage normalization to handle nonuniform sampling in both data and landmark sets. It demonstrates that, under a manifold model with a frame bundle structure, LA‑VDM can accurately recover parallel transport from a point cloud and asymptotically converges to the connection Laplacian. Experiments on simulated data and a nonlocal image denoising application confirm the method’s performance and accuracy.
The growing number of medical vision foundation models highlights the need for effective model selection. However, mainstream selection methods rely on exhaustive fine-tuning, which is computationally expensive.
arXiv:2605. 24395v2 Announce Type: replace Abstract: Alignment plays a fundamental role in many machine learning problems, such as multi-network analysis, multimodal learning, and point cloud registration.
BINDER is a new probabilistic model for medical image registration that builds on mutual information and uses latent voxel‑wise correspondences to enable closed‑form iterative updates. The approach yields a demons‑like optimization algorithm that performs robustly on both monomodal and multimodal tasks, and a sampler that quantifies uncertainty in high‑dimensional 3D deformations. The authors provide the code on GitHub for public use.
We introduce a mathematical framework for shape comparison based on mapping functions from the shape domain to a common reference domain. This Push-Forward Transform enables invariant and robust comparison of shapes, preserving intrinsic geometric information.