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Gromov-Monge Flow Matching for Equivariant Graph Generation
Moritz Piening, Christian Wald
Graphs are invariant under node permutations, motivating the use of permutation-equivariant architectures in generative models. In flow matching, however, symmetry may also enter t…
Generalized Wasserstein Flow Matching: Transport Plans, Everywhere, All at Once
Moritz Piening, Richard Duong, Gabriele Steidl
Flow matching has recently emerged as a flexible and efficient framework for generative modelling by learning deterministic transport dynamics between probability measures. In this…
Slicing Wasserstein Over Wasserstein Via Functional Optimal Transport
Moritz Piening, Robert Beinert
Wasserstein distances define a metric between probability measures on arbitrary metric spaces, including meta-measures (measures over measures). The resulting Wasserstein over Wass…
A Novel Sliced Fused Gromov-Wasserstein Distance
Moritz Piening, Robert Beinert
The Gromov--Wasserstein (GW) distance and its fused extension (FGW) are powerful tools for comparing heterogeneous data. Their computation is, however, challenging since both dista…
Slicing the Gaussian Mixture Wasserstein Distance
Moritz Piening, Robert Beinert
Gaussian mixture models (GMMs) are widely used in machine learning for tasks such as clustering, classification, image reconstruction, and generative modeling. A key challenge in w…
Joint Metric Space Embedding by Unbalanced OT with Gromov-Wasserstein Marginal Penalization
Florian Beier, Moritz Piening, Robert Beinert +1
We propose a new approach for unsupervised alignment of heterogeneous datasets, which maps data from two different domains without any known correspondences to a common metric spac…