Mar 2026· arXiv.org· Vol abs/2603.21247· 0 citations· 25 references
MathematicsComputer SciencePhysics
TL;DR
Under a manifold model with the frame bundle structure, it is shown that it can accurately recover the parallel transport with landmark-constrained diffusion from a point cloud, and hence asymptotically LA-VDM converges to the connection Laplacian.
Abstract
We propose a landmark-constrained algorithm, LA-VDM (Landmark Accelerated Vector Diffusion Maps), to accelerate the Vector Diffusion Maps (VDM) framework built upon the Graph Connection Laplacian (GCL), which captures pairwise connection relationships within complex datasets. LA-VDM introduces a novel two-stage normalization that effectively address nonuniform sampling densities in both the data and the landmark sets. Under a manifold model with the frame bundle structure, we show that we can accurately recover the parallel transport with landmark-constrained diffusion from a point cloud, and hence asymptotically LA-VDM converges to the connection Laplacian. The performance and accuracy of LA-VDM are demonstrated through experiments on simulated datasets and an application to nonlocal image denoising.
The increasing availability of trajectory data is often hampered by sparsity and noise. Existing trajectory recovery methods are further limited by either information loss from coordinate discretization into location IDs, or the inefficiency of conventional diffusion models that require a lengthy denoising process from...
Jia-Qi Duan, Shengwei Tian, Long Yu et al.· Proceedings of the Thirty-Fi...· 0 citations
The proposed update incorporates the objective gradient inside the denoising step, yielding an inference-time method that uses only a pretrained denoiser and gradient evaluations and is analyzed as an inexact projected-gradient method for constrained optimization over learned feasible geometries.
R. Zhang, Jiawei Zhang, Gioele Zardini et al.· 0 citations
Observation Operator Diffusion is proposed, a unified framework that aligns both the supervision trajectory and feature refinement with the intrinsic recovery order of image structures and introduces GL-CoDA, a decoder that injects scale-specific Gaussian-Lanczos observations across decoding stages for coarse-to-fine f...
Shaojie Guo, Li-Chen Ma, Haoyang Tong et al.· 1 citation
iLogMap is introduced, a method for computing GPCs in curved domains that recasts the angular component of the logarithmic map to a ground-state magnetic eigenproblem over the circumferential direction field of geodesic distance, enabling cylindrical and spherical parameterizations in tetrahedral meshes.
Tomás Banduc, Simone Pezzuto, F. S. Costabal· 0 citations
Recently, Drifting Models and Wasserstein Gradient Flows have attracted substantial attention because they move iterative distributional refinement to training and amortize it into a generator, enabling fast inference. However, existing formulations have been developed largely for continuous Euclidean domains, such as...
David Li, Chanhyuk Lee, Jaehoon Yoo et al.· 0 citations
This work generalizes FM to the broader class of location-scale families for handling data inhomogeneity and introduces a novel class of probability paths defined as geodesics on the manifold of probability distributions, called probabilistic geodesic flow matching.
Ze-Yuan Yu, Zhi Chang, Shi-Wei Lan· 0 citations
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