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Diffusion models create data from noise by inverting the forward paths of data towards noise and have emerged as a powerful generative modeling technique for high-dimensional, perceptual data such as images and videos. Rectified flow is a…

Diffusion models are primarily trained for image synthesis, yet their denoising trajectories encode rich, spatially aligned visual priors. In this paper, we demonstrate that these priors can be utilized for text-conditioned semantic and…

Automated 3D scene generation is pivotal for applications spanning virtual reality, digital content creation, and Embodied AI. While computer graphics prioritizes aesthetic layouts, vision and robotics demand scenes that mirror real-world…

Diffusion Probabilistic Models (DPMs) have recently demonstrated impressive results on various generative tasks.Despite its promises, the learned representations of pre-trained DPMs, however, have not been fully understood. In this paper,…

Recent advances in diffusion models have demonstrated their remarkable ability to capture complex image distributions, but the geometric properties of the learned data manifold remain poorly understood. We address this gap by introducing a…

Data attribution for generative models seeks to quantify the influence of individual training examples on model outputs. Existing methods for diffusion models typically require access to model gradients or retraining, limiting their…

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…

We introduce the Linearized Diffusion Map (LDM), a novel linear dimensionality reduction method constructed via a linear approximation of the diffusion-map kernel. LDM integrates the geometric intuition of diffusion-based nonlinear methods…

Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…

Representation learning is a widely adopted framework for learning in data-scarce environments to obtain a feature extractor or representation from various different yet related tasks. Despite extensive research on representation learning,…

Text-to-image generation models have achieved remarkable capabilities in synthesizing images, but often struggle to provide fine-grained control over the output. Existing guidance approaches, such as segmentation maps and depth maps,…

This work introduces the Grassmannian Diffusion Maps, a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the…

Image classification serves as the cornerstone of computer vision, traditionally achieved through discriminative models based on deep neural networks. Recent advancements have introduced classification methods derived from generative…

Text-to-image diffusion models generate highly detailed textures, yet they often rely on surface appearance and fail to follow strict geometric constraints, particularly when those constraints conflict with the style implied by the text…

The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks. Recently, several works have introduced generalizations of the scattering transform for non-Euclidean…

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical…

Understanding and predicting interface diffusion phenomena in materials is crucial for various industrial applications, including semiconductor manufacturing, battery technology, and catalysis. In this study, we propose a novel approach…

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central…

Kernel-based non-linear dimensionality reduction methods, such as Local Linear Embedding (LLE) and Laplacian Eigenmaps, rely heavily upon pairwise distances or similarity scores, with which one can construct and study a weighted graph…

Convolutional Neural Networks (CNN) have been regarded as a powerful class of models for visual recognition problems. Nevertheless, the convolutional filters in these networks are local operations while ignoring the large-range dependency.…