Related papers: Lipschitz Singularities in Diffusion Models

Diffusion models have recently gained unprecedented attention in the field of image synthesis due to their remarkable generative capabilities. Notwithstanding their prowess, these models often incur substantial computational costs,…

Extracting dynamic models from data is of enormous importance in understanding the properties of unknown systems. In this work, we employ Lipschitz neural networks, a class of neural networks with a prescribed upper bound on their Lipschitz…

The ubiquity of missing data has sparked considerable attention and focus on tabular data imputation methods. Diffusion models, recognized as the cutting-edge technique for data generation, demonstrate significant potential in tabular data…

Diffusion Purification, purifying noised images with diffusion models, has been widely used for enhancing certified robustness via randomized smoothing. However, existing frameworks often grapple with the balance between efficiency and…

Linear diffusion processes serve as canonical continuous-time models for dynamic decision-making under uncertainty. These systems evolve according to drift matrices that specify the instantaneous rates of change in the expected system…

Diffusion models have achieved remarkable success in text-to-speech (TTS), even in zero-shot scenarios. Recent efforts aim to address the trade-off between inference speed and sound quality, often considered the primary drawback of…

Diffusion models have seen immense success in modelling continuous data across a range of domains such as vision and audio. Despite the challenges of adapting diffusion models to discrete data, recent work explores their application to text…

Diffusion models have demonstrated impressive generative capabilities, but their \textit{exposure bias} problem, described as the input mismatch between training and sampling, lacks in-depth exploration. In this paper, we systematically…

In our pursuit of finding a zero for a monotone and Lipschitz continuous operator $M : \R^n \rightarrow \R^n$ amidst noisy evaluations, we explore an associated differential equation within a stochastic framework, incorporating a correction…

Diffusion models (DMs) have become the dominant paradigm of generative modeling in a variety of domains by learning stochastic processes from noise to data. Recently, diffusion denoising bridge models (DDBMs), a new formulation of…

Estimating and disentangling epistemic uncertainty, uncertainty that is reducible with more training data, and aleatoric uncertainty, uncertainty that is inherent to the task at hand, is critically important when applying machine learning…

Recent progress in text-to-image (TTI) systems, such as StableDiffusion, Imagen, and DALL-E 2, have made it possible to create realistic images with simple text prompts. It is tempting to use these systems to eliminate the manual task of…

Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…

Denoising Diffusion Models (DDMs) have become a popular tool for generating high-quality samples from complex data distributions. These models are able to capture sophisticated patterns and structures in the data, and can generate samples…

Diffusion models for continuous state spaces based on Gaussian noising processes are now relatively well understood from both practical and theoretical perspectives. In contrast, results for diffusion models on discrete state spaces remain…

The recent wave of large-scale text-to-image diffusion models has dramatically increased our text-based image generation abilities. These models can generate realistic images for a staggering variety of prompts and exhibit impressive…

Score-based diffusion models (SBDM) have recently emerged as state-of-the-art approaches for image generation. Existing SBDMs are typically formulated in a finite-dimensional setting, where images are considered as tensors of finite size.…

We consider the problem of the discrete-time approximation of the solution of a one-dimensional SDE with piecewise locally Lipschitz drift and continuous diffusion coefficients with polynomial growth. In this paper, we study the strong…

Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…

Image generative models, particularly diffusion-based models, have surged in popularity due to their remarkable ability to synthesize highly realistic images. However, since these models are data-driven, they inherit biases from the…