Manifold Diffusion

Manifold diffusion techniques leverage the underlying geometric structure of data, often represented as a manifold, to improve machine learning algorithms. Current research focuses on applying these methods to diverse problems, including federated learning, cross-domain regression, anomaly detection, and image generation, often employing diffusion models, energy-based models, or variational autoencoders adapted for manifold learning. This approach offers advantages in efficiency, robustness, and generalization, particularly in scenarios with high-dimensional or non-Euclidean data, impacting fields ranging from remote sensing to medical image analysis. The development of efficient algorithms for manifold-based processing and the exploration of their theoretical properties remain active areas of investigation.

Papers

June 12, 2024

Nonconvex Federated Learning on Compact Smooth Submanifolds With Heterogeneous Data
Jiaojiao Zhang, Jiang Hu, Anthony Man-Cho So, Mikael Johansson
Heterogeneous Data Riemannian Gradient Manifold Dimension Manifold Diffusion Manifold Optimization

May 1, 2024

Get Your Embedding Space in Order: Domain-Adaptive Regression for Forest Monitoring
Sizhuo Li, Dimitri Gominski, Martin Brandt, Xiaoye Tong, Philippe Ciais
Cross Domain Deep Space Order Matter Image Regression Forest Monitoring Deep Regression Forest Manifold Diffusion

January 12, 2024

Adversarial Examples are Misaligned in Diffusion Model Manifolds
Peter Lorenz, Ricard Durall, Janis Keuper
Diffusion Model Adversarial Attack Adversarial Example Adversarial Robustness Adversarial Instance Manifold Diffusion

November 28, 2023

Manifold Preserving Guided Diffusion
Yutong He, Naoki Murata, Chieh-Hsin Lai, Yuhta Takida, Toshimitsu Uesaka, Dongjun Kim, Wei-Hsiang Liao, Yuki Mitsufuji, J. Zico Kolter, Ruslan Salakhutdinov, Stefano Ermon
Latent Diffusion Model Classifier Free Guidance Conditional Image Generation Manifold Diffusion

October 28, 2023

Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approach
Sangwoong Yoon, Young-Uk Jin, Yung-Kyun Noh, Frank C. Park
Anomaly Detection Negative Sampling Energy Based Model Low Dimensional Manifold Manifold Diffusion

May 24, 2023

Manifold Diffusion Fields
Ahmed A. Elhag, Yuyang Wang, Joshua M. Susskind, Miguel Angel Bautista
Diffusion Model Class Manifold Dimensional Manifold Spectral Learning Manifold Diffusion

January 15, 2023

Segmenting thalamic nuclei from manifold projections of multi-contrast MRI
Chang Yan, Muhan Shao, Zhangxing Bian, Anqi Feng, Yuan Xue, Jiachen Zhuo, Rao P. Gullapalli, Aaron Carass, Jerry L. Prince
Multi Contrast Quantitative Segmentation Brain Parcellation Tissue Phenotyping Manifold Diffusion Subcortical Segmentation

November 20, 2022

Convolutional Filtering on Sampled Manifolds
Zhiyang Wang, Luana Ruiz, Alejandro Ribeiro
Convolutional Filter Statistical Manifold Manifold Diffusion Manifold Sampling

September 30, 2022

Hyperbolic VAE via Latent Gaussian Distributions
Seunghyuk Cho, Juyong Lee, Dongwoo Kim
Lung VAE Statistical Manifold Gaussian Latent Manifold Diffusion \Beta$ VAE