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: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
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.
By Zichen Liu, Wei Zhang, Christof Sch\"utte, Tiejun Li
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...
By Xinyu Tian, Xiaotong Shen
arXiv:2606. 07036v1 Announce Type: cross Abstract: Synthetic histopathology image generation addresses critical challenges in computational pathology, including patient privacy and the growing need for large-scale training data for foundation models.
By Won June Cho, Daeky Jeong, Hyeongyeol Lim, Hongjun Yoon
arXiv:2509. 24710v2 Announce Type: replace-cross Abstract: Score-based diffusion models are a highly effective method for generating samples from a distribution of images.
By Dennis Elbr\"achter, Giovanni S. Alberti, Matteo Santacesaria
arXiv:2501. 09876v3 Announce Type: replace-cross Abstract: Generative modeling aims to generate new data samples that resemble a given dataset.
By Wonjun Lee, Riley C. W. O'Neill, Dongmian Zou, Jeff Calder, Gilad Lerman
arXiv:2608.31028v1 Announce Type: cross
Abstract: Scientific discovery often requires reasoning over competing hypotheses that are consistent with experimental observations. For mixed-variable and co...
By James Crowley, Faez Ahmed, Anton van Beek
arXiv:2601.21831v3 Announce Type: replace
Abstract: We propose a geometric latent-subspace framework for generative modeling of discrete data. Specifically, we introduce latent subspaces in the expon...
By Daniel Gonzalez-Alvarado, Jonas Cassel, Stefania Petra, Christoph Schn\"orr
arXiv:2602. 09708v2 Announce Type: replace-cross Abstract: We propose physics-informed spectral diffusion (PISD), a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of partial differential equations (PDEs) conditioned on partial observations, which includes, in particular, forward and inverse PDE problems.
By Davide Gallon, Philippe von Wurstemberger, Patrick Cheridito, Arnulf Jentzen
arXiv:2603. 22962v3 Announce Type: replace Abstract: We study the theoretical behavior of denoising score matching--the learning task associated to diffusion models--when the data distribution is supported on a low-dimensional manifold and the score is parameterized using a random feature neural network.
By Anand Jerry George, Nicolas Macris
arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.
By Andrew Gracyk