Related papers: Diffusion Models and the Manifold Hypothesis: Log-…
Under the data manifold hypothesis, high-dimensional data are concentrated near a low-dimensional manifold. We study the problem of Riemannian optimization over such manifolds when they are given only implicitly through the data…
We propose closed-form conditional diffusion models for data assimilation. Diffusion models use data to learn the score function (defined as the gradient of the log-probability density of a data distribution), allowing them to generate new…
Score-based generative models, which transform noise into data by learning to reverse a diffusion process, have become a cornerstone of modern generative AI. This paper contributes to establishing theoretical guarantees for the probability…
Most recent unsupervised non-rigid 3D shape matching methods are based on the functional map framework due to its efficiency and superior performance. Nevertheless, respective methods struggle to obtain spatially smooth pointwise…
Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results…
The latent space of diffusion model mostly still remains unexplored, despite its great success and potential in the field of generative modeling. In fact, the latent space of existing diffusion models are entangled, with a distorted mapping…
Diffusion models have been leveraged to perform adversarial purification and thus provide both empirical and certified robustness for a standard model. On the other hand, different robustly trained smoothed models have been studied to…
Diffusion Models (DMs), also referred to as score-based diffusion models, utilize neural networks to specify score functions. Unlike most other probabilistic models, DMs directly model the score functions, which makes them more flexible to…
Diffusion models have recently achieved remarkable success in generative modeling, yet they are commonly formulated as black-box stochastic systems with limited interpretability and few structural guarantees. In this paper, we establish a…
High-dimensional data are often assumed to lie on lower-dimensional manifolds. We study how to construct diffusion processes on this data manifold using only point cloud samples and without access to charts, projections, or other geometric…
Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling and for estimating properties of scientific systems. The diffusion processes that are tractable center on linear processes with a…
Diffusion models have attained remarkable success in the domains of image generation and editing. It is widely recognized that employing larger inversion and denoising steps in diffusion model leads to improved image reconstruction quality.…
Diffusion models are powerful deep generative models, but unlike classical models, they lack an explicit low-dimensional latent space that parameterizes the data manifold. This absence makes it difficult to perform manifold-aware…
The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and…
Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…
Domain generalization (DG) for object detection aims to enhance detectors' performance in unseen scenarios. This task remains challenging due to complex variations in real-world applications. Recently, diffusion models have demonstrated…
Denoising diffusion models are a novel class of generative algorithms that achieve state-of-the-art performance across a range of domains, including image generation and text-to-image tasks. Building on this success, diffusion models have…
Flat minima, known to enhance generalization and robustness in supervised learning, remain largely unexplored in generative models. In this work, we systematically investigate the role of loss surface flatness in generative models, both…
Diffusion models accomplish remarkable success in data generation tasks across various domains. However, the iterative sampling process is computationally expensive. Consistency models are proposed to learn consistency functions to map from…
Imperfect score-matching leads to a shift between the training and the sampling distribution of diffusion models. Due to the recursive nature of the generation process, errors in previous steps yield sampling iterates that drift away from…