A framework for learning augmented Riemannian flow maps that enables both fast sampling and tractable likelihood evaluation on curved manifolds and provides a scalable, geometry-consistent approach for generative modeling and likelihood evaluation in these regimes.
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
MoNO is proposed, a training-free method that performs Manifold-constrained Noise Optimization on a low-dimensional, quality-stabilizing noise manifold that combines Riemannian updates on an affine low-frequency sphere to preserve prior likelihood and fix unstable high-frequency components by construction.
Qi-Tan Shi, Cheng Jin, Zi-Yuan Liu et al.· arXiv.org· 1 citation
Divergence-based regularization and Sharpness-Aware Minimization (SAM) are two prominent approaches for improving generalization in deep learning, both motivated by robustness to perturbations. However, their relationship has remained largely unexplored. Building on classical second-order expansions of $f$-divergences,...
This work leverage pretrained score-based models as geometric priors and learn a vector field that evolves data along score-induced interpolation paths that supports generation at arbitrary timestamps and temporal super-resolution beyond the discretization of the training data.
Jan Tauberschmidt, Brian B. Moser, Stanislav Frolov et al.· 0 citations
This work introduces Riemannian Orthogonally Decoupled Regularization (RODR) to reformulate the optimization trajectory by disentangling the normal (fitting) and tangential (distribution) components and establishes a generic and interpretable framework for disentangled geometric optimization in point cloud processing.
This work develops a bootstrap algorithm on Riemannian manifolds that is both computationally efficient and accurate for hypothesis testing and confidence region construction, and establishes high-order asymptotics under an appropriate coordinate representation induced by a second-order retraction.
Cheng-Zhu Huang, An-Ru R. Zhang· Annals of Statistics· 0 citations
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