Related papers: Diffusion Generative Modeling on Lie Group Represe…
Score-based diffusion models generate new samples by learning the score function associated with a diffusion process. While the effectiveness of these models can be theoretically explained using differential equations related to the…
Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise,…
In the first part of this paper, we consider a family of continuous-time dynamical systems coupled with diffusion-transmutation processes. Under certain conditions, such randomly perturbed dynamical systems can be interpreted as an averaged…
Generative diffusion models, famous for their performance in image generation, are popular in various cross-domain applications. However, their use in the communication community has been mostly limited to auxiliary tasks like data modeling…
Diffusion models have shown impressive performance for image generation, often times outperforming other generative models. Since their introduction, researchers have extended the powerful noise-to-image denoising pipeline to discriminative…
We adopt a Gamma and Malliavin Calculi point of view in order to generalize Score-based diffusion Generative Models (SGMs) to an infinite-dimensional abstract Hilbertian setting. Particularly, we define the forward noising process using…
Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…
Joint machine learning models that allow synthesizing and classifying data often offer uneven performance between those tasks or are unstable to train. In this work, we depart from a set of empirical observations that indicate the…
Neural networks struggle with image classification when biases are learned and misleads correlations, affecting their generalization and performance. Previous methods require attribute labels (e.g. background, color) or utilizes Generative…
This paper gives direct derivations of the differential equations and likelihood formulas of diffusion models assuming only knowledge of Gaussian distributions. A VAE analysis derives both forward and backward stochastic differential…
We analyze the time reversed dynamics of generative diffusion models. If the exact empirical score function is used in a regime of large dimension and exponentially large number of samples, these models are known to undergo transitions…
In this work, we look at Score-based generative models (also called diffusion generative models) from a geometric perspective. From a new view point, we prove that both the forward and backward process of adding noise and generating from…
Diffusion models suffer from slow sample generation at inference time. Therefore, developing a principled framework for fast deterministic/stochastic sampling for a broader class of diffusion models is a promising direction. We propose two…
Diffusion models have emerged as powerful deep generative techniques, producing high-quality and diverse samples in applications in various domains including audio. While existing reviews provide overviews, there remains limited in-depth…
Deep Gaussian processes (DGPs) provide a robust paradigm for Bayesian deep learning. In DGPs, a set of sparse integration locations called inducing points are selected to approximate the posterior distribution of the model. This is done to…
Diffusion-based generative graph models have been proven effective in generating high-quality small graphs. However, they need to be more scalable for generating large graphs containing thousands of nodes desiring graph statistics. In this…
We introduce generative models for accelerating simulations of complex systems through learning and evolving their effective dynamics. In the proposed Generative Learning of Effective Dynamics (G-LED), instances of high dimensional data are…
Score-based generative models (SGMs) have recently shown impressive results for difficult generative tasks such as the unconditional and conditional generation of natural images and audio signals. In this work, we extend these models to the…
We propose a hybrid generative model for efficient sampling of high-dimensional, multimodal probability distributions for Bayesian inference. Traditional Monte Carlo methods, such as the Metropolis-Hastings and Langevin Monte Carlo sampling…
We provide the first polynomial-time convergence guarantees for the probability flow ODE implementation (together with a corrector step) of score-based generative modeling. Our analysis is carried out in the wake of recent results obtaining…