arXiv Machine Learning
A Likely Geometry of Generative Models
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ReSFlow: Rectifying Categorical Flows on Statistical Manifolds for One-Step Generation
ReSFlow is a generative model that learns geodesic trajectories on statistical manifolds to enable one‑step categorical generation. By rectifying continuous‑time flows to follow intrinsic Riemannian geometry, it reduces transport cost and eliminates the need for multi‑step numerical integration. Experiments across image, text, and biological datasets show that ReSFlow achieves superior one‑step generation quality compared to prior methods.
arXiv Machine Learning
Jul 14
Riemannian Denoising Diffusion Probabilistic Models
arXiv:2505. 04338v3 Announce Type: replace Abstract: We propose Riemannian Denoising Diffusion Probabilistic Models (RDDPMs) for learning distributions on submanifolds of Euclidean space that are level sets of functions, including most of the manifolds relevant to applications.
arXiv Machine Learning
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Riemannian Metric Matching for Scalable Geometric Modeling of Distributions
arXiv:2606. 14334v1 Announce Type: new Abstract: High-dimensional datasets often concentrate near low-dimensional structures, but estimating their geometry from samples typically relies on graphs and kernels that scale poorly with dataset size and dimension.
arXiv AI
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Riemannian-Manifold Steering: Geometry-Aware Generative Autoencoders for Label-Free Steering
arXiv:2605. 24942v2 Announce Type: replace-cross Abstract: Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention transformations without learning an explicit geometry over paths in activation space.
arXiv Machine Learning
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When Riemann flows with Wasserstein: Generative Modeling of Probability Distributions on Manifolds
arXiv:2609.25659v1 Announce Type: new Abstract: Many scientific datasets, such as molecular conformational ensembles or single-cell tissue measurements, are naturally modeled as meta-distributions: d...
arXiv Machine Learning
5d ago
Learning Normal Coordinates on Riemannian Manifolds with Flow Charts
The paper introduces flow charts, a conditional invertible neural network designed to approximate normal coordinates on Riemannian manifolds, enabling fast Euclidean approximations of exponential and logarithmic maps. It presents a novel nonnegative loss function that is zero exactly when the chart is normal, and demonstrates that flow charts match or surpass specialized neural geodesic interpolators across sixteen synthetic and data‑derived geometries. When pretrained, flow charts achieve a median 60–70× speedup over numerical baselines while maintaining comparable logarithmic map estimation error and improving numerical geodesic solver accuracy.