Related papers: (Deep) Generative Geodesics
Graph diffusion models have made significant progress in learning structured graph data and have demonstrated strong potential for predictive tasks. Existing approaches typically embed node, edge, and graph-level features into a unified…
The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing…
Approximating complex probability distributions, such as Bayesian posterior distributions, is of central interest in many applications. We study the expressivity of geometric Gaussian approximations. These consist of approximations by…
The commonly used latent space embedding techniques, such as Principal Component Analysis, Factor Analysis, and manifold learning techniques, are typically used for learning effective representations of homogeneous data. However, they do…
Graph generative models are a highly active branch of machine learning. Given the steady development of new models of ever-increasing complexity, it is necessary to provide a principled way to evaluate and compare them. In this paper, we…
Realistic human geometry generation is an important yet challenging task, requiring both the preservation of fine clothing details and the accurate modeling of clothing-body interactions. To tackle this challenge, we build upon Geometry…
Deep metric learning aims to learn an embedding space where the distance between data reflects their class equivalence, even when their classes are unseen during training. However, the limited number of classes available in training…
Deep generative models learned through adversarial training have become increasingly popular for their ability to generate naturalistic image textures. However, aside from their texture, the visual appearance of objects is significantly…
Probabilistic generative models can be used for compression, denoising, inpainting, texture synthesis, semi-supervised learning, unsupervised feature learning, and other tasks. Given this wide range of applications, it is not surprising…
Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a ``noising'' stage, whereby a diffusion is used to gradually…
Generative models based on diffusion have become the state of the art in the last few years, notably for image generation. Here, we analyse them in the high-dimensional limit, where data are formed by a very large number of variables. We…
In image generation, generative models can be evaluated naturally by visually inspecting model outputs. However, this is not always the case for graph generative models (GGMs), making their evaluation challenging. Currently, the standard…
Generalized tensor analysis in the sense of Colombeau's construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of…
We introduce and motivate generative modeling as a central task for machine learning and provide a critical view of the algorithms which have been proposed for solving this task. We overview how generative modeling can be defined…
Artificial data synthesis is currently a well studied topic with useful applications in data science, computer vision, graphics and many other fields. Generating realistic data is especially challenging since human perception is highly…
The geometric approach to optimal transport and information theory has triggered the interpretation of probability densities as an infinite-dimensional Riemannian manifold. The most studied Riemannian structures are Otto's metric, yielding…
This thesis is concerned with extending the idea of geodesic completeness from pseudo-Riemannian to complex geometry: we take, however a completely holomorphicpoint of view; that is to say, a 'metric' will be a (meromorphic) symmetric…
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…
In this paper, we introduce a convenient framework for studying (adversarial) generative models from a statistical perspective. It consists in modeling the generative device as a smooth transformation of the unit hypercube of a dimension…
Generative models are typically evaluated by direct inspection of their generated samples, e.g., by visual inspection in the case of images. Further evaluation metrics like the Fr\'echet inception distance or maximum mean discrepancy are…