Towards Variational Flow Matching on General Geometries

• URL: http://arxiv.org/abs/2502.12981v1
• Date: Tue, 18 Feb 2025 16:02:10 GMT
• Title: Towards Variational Flow Matching on General Geometries
• Authors: Olga Zaghen, Floor Eijkelboom, Alison Pouplin, Erik J. Bekkers,
• Abstract summary: RG-VFM captures geometric structure more effectively than Euclidean VFM and baseline methods. It is a robust framework for manifold-aware generative modeling.
• Score: 7.5684697258210685
• License:
• Abstract: We introduce Riemannian Gaussian Variational Flow Matching (RG-VFM), an extension of Variational Flow Matching (VFM) that leverages Riemannian Gaussian distributions for generative modeling on structured manifolds. We derive a variational objective for probability flows on manifolds with closed-form geodesics, making RG-VFM comparable - though fundamentally different to Riemannian Flow Matching (RFM) in this geometric setting. Experiments on a checkerboard dataset wrapped on the sphere demonstrate that RG-VFM captures geometric structure more effectively than Euclidean VFM and baseline methods, establishing it as a robust framework for manifold-aware generative modeling.

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