Related papers: On Convolutions, Intrinsic Dimension, and Diffusio…
Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…
Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…
Most recent works focus on answering first order logical queries to explore the knowledge graph reasoning via multi-hop logic predictions. However, existing reasoning models are limited by the circumscribed logical paradigms of training…
In this work, we present FRIGID, a framework with a novel diffusion language model that generates molecular structures conditioned on mass spectra via intermediate fingerprint representations and determined chemical formulae, training at…
Denoising diffusion models have spurred significant gains in density modeling and image generation, precipitating an industrial revolution in text-guided AI art generation. We introduce a new mathematical foundation for diffusion models…
While many unsupervised learning models focus on one family of tasks, either generative or discriminative, we explore the possibility of a unified representation learner: a model which uses a single pre-training stage to address both…
High-dimensional datasets often exhibit low-dimensional geometric structures, as suggested by the manifold hypothesis, which implies that data lie on a smooth manifold embedded in a higher-dimensional ambient space. While this insight…
Recovering high-dimensional signals from corrupted measurements is a central challenge in inverse problems. Recent advances in generative diffusion models have shown remarkable empirical success in providing strong data-driven priors, but…
Diffusion-based language models are emerging as a promising alternative to autoregressive LMs: they approach the competence of autoregressive LMs while offering nuanced controllability at inference time. While autoregressive LMs have…
Out-of-distribution (OOD) generalization has long been a challenging problem that remains largely unsolved. Gaussian processes (GP), as popular probabilistic model classes, especially in the small data regime, presume strong OOD…
Representation learning is all about discovering the hidden modular attributes that generate the data faithfully. We explore the potential of Denoising Diffusion Probabilistic Model (DM) in unsupervised learning of the modular attributes.…
Real-world data generation often involves complex inter-dependencies among instances, violating the IID-data hypothesis of standard learning paradigms and posing a challenge for uncovering the geometric structures for learning desired…
Diffusion models power leading generative AI, but when and how they memorize training data, especially on low-dimensional manifolds, remains unclear. We find memorization emerges gradually, not abruptly: as data become scarce, diffusion…
A common observation in data-driven applications is that high dimensional data has a low intrinsic dimension, at least locally. In this work, we consider the problem of estimating a $d$ dimensional sub-manifold of $\mathbb{R}^D$ from a…
Generative models have enabled intuitive image creation and manipulation using natural language. In particular, diffusion models have recently shown remarkable results for natural image editing. In this work, we propose to apply diffusion…
Diffusion models have recently emerged as powerful tools for missing data imputation by modeling the joint distribution of observed and unobserved variables. However, existing methods, typically based on stochastic denoising diffusion…
Diffusion models have recently been investigated as powerful generative solvers for image dehazing, owing to their remarkable capability to model the data distribution. However, the massive computational burden imposed by the retraining of…
We introduce Hodge Diffusion Maps, a novel manifold learning algorithm designed to analyze and extract topological information from high-dimensional data-sets. This method approximates the exterior derivative acting on differential forms,…
Despite the remarkable success, recent reconstruction-based anomaly detection (AD) methods via diffusion modeling still involve fine-grained noise-strength tuning and computationally expensive multi-step denoising, leading to a fundamental…
Diffusion models have established themselves as state-of-the-art generative models across various data modalities, including images and videos, due to their ability to accurately approximate complex data distributions. Unlike traditional…