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...
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.
arXiv:2510. 01015v3 Announce Type: cross Abstract: Wasserstein metrics are increasingly adopted as similarity scores for images.
arXiv:2510.26266v3 Announce Type: replace Abstract: The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a p...
The paper introduces Constant‑Curvature Sliced Gromov‑Wasserstein (CCSGW), a new divergence for aligning probability distributions on heterogeneous constant‑curvature spaces such as hyperbolic and spherical manifolds. It extends sliced Gromov‑Wasserstein by adding geodesic‑based one‑dimensional projections for spherical spaces, enabling efficient and principled comparison across manifolds with different curvatures while preserving intrinsic geometric relationships. The authors provide theoretical analysis showing that CCSGW controls intrinsic geometric discrepancy and demonstrate consistent performance gains when integrated into mixed‑curvature learning tasks like graph anomaly detection, node classification, and multimodal learning.
arXiv:2602. 10099v2 Announce Type: replace Abstract: Leveraging representation encoders for generative modeling offers a path for efficient, high-fidelity synthesis.
The paper develops a statistical framework showing that empirical score matching can achieve minimax optimal performance for diffusion generative models when data lie on a low‑dimensional manifold. It establishes convergence rates for empirical risk minimization over constrained Sobolev classes and demonstrates that the resulting score estimators yield minimax optimal Wasserstein‑1 rates for the generated distribution, up to logarithmic factors. The analysis reveals that the statistical rates depend on the intrinsic dimension of the data manifold rather than its ambient dimension, providing conditions under which score‑based generative modeling generalizes rather than overfits.
The paper investigates training objectives for denoising-based generative models, focusing on loss weighting and output parameterization such as noise-, clean image-, and velocity-based formulations. It conducts a systematic numerical study across synthetic datasets with controlled geometry and real image data, evaluating denoising accuracy via PSNR and generative quality via FID. The goal is to disentangle how training choices interact with data manifold dimensionality, model architecture, and dataset size, offering practical design insights rather than proposing a new method.
arXiv:2602.19600v2 Announce Type: replace Abstract: Many high-dimensional datasets concentrate near a low-dimensional structure embedded in the ambient space. Generative models for such data must con...
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.
The paper investigates flow matching on manifolds, focusing on the 1D flat torus. It identifies a failure mode caused by a property called compatibility, where a likelihood-based flow matching objective can be globally optimized by a velocity field that actually pushes samples away from the data distribution. The authors propose a new compatible objective built from an exponential family over endpoints, which restricts the velocity field to feasible values on compact manifolds and improves performance on high-dimensional product tori, geospatial benchmarks on the sphere, and a large human pose dataset.
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.