Advances in Diffusion Models and Manifold Learning

The field of diffusion models and manifold learning is rapidly advancing, with a focus on improving the efficiency and effectiveness of these models. Recent developments have centered around addressing key challenges, such as degeneracies in latent interpolation, score function singularity, and the need for more expressive and regularized models. Researchers are exploring new methodologies, including the use of deep learning techniques, Riemannian manifolds, and adaptive sampling algorithms, to enhance the performance and interpretability of these models. Notable papers in this area include those that propose novel approaches to diffusion models, such as the use of non-isotropic noise and tangential-only loss functions, as well as those that develop new manifold learning techniques, such as Isometric Immersion Kernel Learning and Manifold Learning with Normalizing Flows. Overall, these advances have the potential to significantly impact a range of applications, from image generation and data augmentation to scientific simulations and parameter inference. Noteworthy papers include:

  • Automated Learning of Semantic Embedding Representations for Diffusion Models, which introduces a multi-level denoising autoencoder framework to expand the representation capacity of diffusion models.
  • IIKL: Isometric Immersion Kernel Learning with Riemannian Manifold for Geometric Preservation, which proposes a novel method for building Riemannian manifolds and isometrically inducing Riemannian metrics from discrete non-Euclidean data.

Sources

Automated Learning of Semantic Embedding Representations for Diffusion Models

Deep Diffusion Maps

IIKL: Isometric Immersion Kernel Learning with Riemannian Manifold for Geometric Preservation

Addressing degeneracies in latent interpolation for diffusion models

Latent Behavior Diffusion for Sequential Reaction Generation in Dyadic Setting

Manifold Learning with Normalizing Flows: Towards Regularity, Expressivity and Iso-Riemannian Geometry

Identifying Memorization of Diffusion Models through p-Laplace Analysis

ConDiSim: Conditional Diffusion Models for Simulation Based Inference

An adaptive sampling algorithm for data-generation to build a data-manifold for physical problem surrogate modeling

A new methodology to decompose a parametric domain using reduced order data manifold in machine learning

On the Well-Posedness of Green's Function Reconstruction via the Kirchhoff-Helmholtz Equation for One-Speed Neutron Diffusion

Improving the Euclidean Diffusion Generation of Manifold Data by Mitigating Score Function Singularity

A generalized discontinuous Hamilton Monte Carlo for transdimensional sampling

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