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.
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.
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.
arXiv:2502. 00336v3 Announce Type: replace Abstract: We theoretically investigate the phenomena of generalization and memorization in diffusion models.
arXiv:2606. 19894v1 Announce Type: new Abstract: The remarkable success of score-based diffusion models has spurred significant efforts to establish their theoretical foundations.
arXiv:2502. 19499v4 Announce Type: replace Abstract: Diffusion models have achieved remarkable progress in various domains with an intriguing ability to produce new data that do not exist in the training set.
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: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: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.
The paper introduces localized diffusion models, which exploit locality structure—sparse conditional dependencies among target variables—to reduce the dimensionality of the score function. By training a localized neural network with a localized score matching loss, the authors demonstrate that diffusion models can achieve dimension‑independent error bounds, balancing statistical and localization errors with a moderate radius. This approach also enables parallel training, potentially improving efficiency for large‑scale applications.
The paper investigates memorization in diffusion models, showing that the empirical score function is a weighted sum of Gaussian score functions with sharp softmax weights, causing individual training samples to dominate and lead to sampling collapse. By approximating this function with a neural network, the authors obtain a smoother representation that generalizes better. They introduce two techniques—Noise Unconditioning and Temperature Smoothing—to further reduce single‑sample dominance, and demonstrate improved generalization across multiple datasets while preserving generation quality.
arXiv:2409. 02426v5 Announce Type: replace Abstract: Despite their empirical success across a wide range of generative tasks, the fundamental principles underlying the ability of diffusion models to learn data distributions are poorly understood.
The paper introduces LA-VDM, a landmark‑constrained algorithm that speeds up Vector Diffusion Maps (VDM) by employing a two‑stage normalization to handle nonuniform sampling in both data and landmark sets. It demonstrates that, under a manifold model with a frame bundle structure, LA‑VDM can accurately recover parallel transport from a point cloud and asymptotically converges to the connection Laplacian. Experiments on simulated data and a nonlocal image denoising application confirm the method’s performance and accuracy.