Proposes diffeomorphic optimization for manifold-constrained problems in generative models via flow maps, with Lie-group extensions for protein design showing metric improvements.
arXiv preprint arXiv:2006.06663 , year=
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PermFlow applies conditional flow matching on the affine subspace of doubly stochastic matrices with a closed-form tangent projector and nearest-target coupling to capture multimodal permutation distributions.
Radial Compensation derives a specific tangent-space base distribution that preserves geodesic-radial likelihoods and chart-invariant Fisher information while maintaining isotropy, decoupling statistical modeling from numerical chart choice in manifold generative models.
citing papers explorer
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Diffeomorphic Optimization
Proposes diffeomorphic optimization for manifold-constrained problems in generative models via flow maps, with Lie-group extensions for protein design showing metric improvements.
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Learning Unbiased Permutations via Flow Matching
PermFlow applies conditional flow matching on the affine subspace of doubly stochastic matrices with a closed-form tangent projector and nearest-target coupling to capture multimodal permutation distributions.
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Radial Compensation: Fixing Radius Distortion in Chart-Based Generative Models on Riemannian Manifolds
Radial Compensation derives a specific tangent-space base distribution that preserves geodesic-radial likelihoods and chart-invariant Fisher information while maintaining isotropy, decoupling statistical modeling from numerical chart choice in manifold generative models.