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arXiv AI

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.

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arXiv Machine Learning
Oct 2

RW-Flow: One-Step Generation on Compact Manifolds via Wasserstein Gradient Flows

RW-Flow presents a new one‑step generative framework for data on compact manifolds, leveraging Wasserstein gradient flows. The authors derive a necessary and sufficient identifiability condition for velocity fields on compact, connected Riemannian manifolds, showing that a symmetric, Lipschitz‑continuous cost function yields identifiability iff its Gibbs kernel is nondegenerate. Experiments on geospatial events, protein and RNA torsion angles, and discretized manifolds demonstrate that RW‑Flow surpasses existing one‑step methods across most benchmark settings.

By Ualibyek Nurgulan, Seungwoo Yoo, Prin Phunyaphibarn, Minhyuk Sung
diffusionbenchmarks
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arXiv Machine Learning
Jun 18

Riemannian MeanFlow for One-Step Generation on Manifolds

arXiv:2603. 10718v3 Announce Type: replace Abstract: Flow Matching enables simulation-free training of generative models on Riemannian manifolds, yet sampling typically still relies on numerically integrating a probability-flow ODE.

By Zichen Zhong, Haoliang Sun, Yukun Zhao, Yongshun Gong, Yilong Yin
diffusion
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arXiv AI
Oct 9

Finsler Flow Matching: Dynamics-Aware Geodesic Interpolation for Single-Snapshot Trajectory Inference

The paper introduces Finsler Flow Matching (FFM), a method for learning continuous stochastic dynamics from discrete Markov transition graphs in single‑cell snapshot data. FFM constructs a Finsler geometry using first and second local moments, learns directed geodesics via neural networks, and employs these to build geometry‑aware stochastic paths that can be simulated without explicit score or flow matching. Benchmark tests show that FFM better recovers intermediate cellular states, especially when dynamics are directional or anisotropic.

By Niklas Canova, Jonas Simon Fleck
diffusionbenchmarks
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arXiv AI
Sep 17

Walking the Score Manifold: Continuous-time Generative Dynamics on Learned Data Manifolds

The paper proposes a continuous‑time generative framework that models time‑dependent data as evolution on a learned data manifold. By using pretrained score‑based models as geometric priors, it learns a vector field that drives data along score‑induced interpolation paths, enabling generation at arbitrary timestamps and temporal super‑resolution. The method includes a regression‑based training objective, a stability‑promoting term interpreted as denoising score matching, and a probabilistic extension for future trajectory distributions, demonstrated on natural video, PDE‑based fields, and molecular dynamics.

By Jan Tauberschmidt, Brian B. Moser, Stanislav Frolov, Andreas Dengel, Andrew B. Duncan, Sebastian J. Vollmer
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arXiv Machine Learning
Oct 2

Manifold-Aware Perturbations for Constrained Generative Modeling

The paper introduces a new method for perturbing data distributions in a way that respects equality constraints, allowing generative models to better handle constrained data. By adjusting the distribution while preserving the manifold geometry, the approach ensures support matches the ambient space dimension. Experiments with diffusion models and normalizing flows demonstrate improved data recovery and stable sampling across several tasks.

By Katherine Keegan, Lars Ruthotto
diffusion
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