arXiv:2409. 18804v3 Announce Type: replace-cross Abstract: Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more applications in science and beyond.
By Iskander Azangulov, George Deligiannidis, Judith Rousseau
We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds. While diffusion models (DMs) have achieved state-of-the-art results in high-dimensional data synthesis, they rely on large training datasets and ignore intrinsic geometric structure.
arXiv:2608. 04827v1 Announce Type: cross Abstract: We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds.
By Yizhu Wang, Mu Niu, Xiaochen Yang
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...
By Frederik M\"obius Rygaard, Shen Zhu, Yinzhu Jin, S{\o}ren Hauberg, Tom Fletcher
Light Entropic Optimal Transport on Riemannian Manifolds introduces ManifoldLightOT, a lightweight method for learning kernel‑induced entropic optimal transport couplings directly on common manifolds such as spheres, tori, SO(3), and SE(3). By constructing geometry‑specific Gibbs kernels and compatible potential parameterizations, the approach yields closed‑form normalization and directly sampleable conditional distributions. The formulation extends naturally to products of manifolds and optimizes potentials from samples using Monte Carlo estimates, demonstrating superior performance over existing manifold OT methods in synthetic and real‑world experiments.
By Xavier Aramayo-Carrasco, Petr Mokrov, Alexander Korotin
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