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[2502.12981] Riemannian Variational Flow Matching for Material and Protein Design
Summary
The paper presents Riemannian Gaussian Variational Flow Matching (RG-VFM), a novel approach for generative modeling on curved manifolds, enhancing material and protein design through improved learning signals and performance.
Why It Matters
This research addresses the limitations of traditional generative modeling methods in curved spaces, which are crucial for accurately modeling complex structures in material and protein design. By introducing RG-VFM, the authors provide a framework that better captures manifold structures, potentially leading to advancements in various scientific fields.
Key Takeaways
- RG-VFM offers a geometric extension of Variational Flow Matching for better generative modeling on manifolds.
- The model incorporates curvature-dependent penalties, enhancing learning signals for endpoint predictions.
- Experiments show RG-VFM outperforms traditional methods in both synthetic and real-world applications.
- The research highlights the importance of geodesic distances in learning on curved spaces.
- Code for RG-VFM is made available, promoting further research and application.
Computer Science > Machine Learning arXiv:2502.12981 (cs) [Submitted on 18 Feb 2025 (v1), last revised 25 Feb 2026 (this version, v3)] Title:Riemannian Variational Flow Matching for Material and Protein Design Authors:Olga Zaghen, Floor Eijkelboom, Alison Pouplin, Cong Liu, Max Welling, Jan-Willem van de Meent, Erik J. Bekkers View a PDF of the paper titled Riemannian Variational Flow Matching for Material and Protein Design, by Olga Zaghen and 6 other authors View PDF HTML (experimental) Abstract:We present Riemannian Gaussian Variational Flow Matching (RG-VFM), a geometric extension of Variational Flow Matching (VFM) for generative modeling on manifolds. Motivated by the benefits of VFM, we derive a variational flow matching objective for manifolds with closed-form geodesics based on Riemannian Gaussian distributions. Crucially, in Euclidean space, predicting endpoints (VFM), velocities (FM), or noise (diffusion) is largely equivalent due to affine interpolations. However, on curved manifolds this equivalence breaks down. We formally analyze the relationship between our model and Riemannian Flow Matching (RFM), revealing that the RFM objective lacks a curvature-dependent penalty -- encoded via Jacobi fields -- that is naturally present in RG-VFM. Based on this relationship, we hypothesize that endpoint prediction provides a stronger learning signal by directly minimizing geodesic distances. Experiments on synthetic spherical and hyperbolic benchmarks, as well as real-wor...
