Related papers: Diffusion Generative Models in Infinite Dimensions

Diffusion Generative Models in Infinite Dimensions

URL: http://arxiv.org/abs/2212.00886v1
Date: Thu, 1 Dec 2022 21:54:19 GMT
Title: Diffusion Generative Models in Infinite Dimensions
Authors: Gavin Kerrigan, Justin Ley, Padhraic Smyth
Abstract summary: We generalize diffusion generative models to operate directly in function space. A significant benefit of our function space point of view is that it allows us to explicitly specify the space of functions we are working in. Our approach allows us to perform both unconditional and conditional generation of function-valued data.
Score: 10.15736468214228
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Diffusion generative models have recently been applied to domains where the available data can be seen as a discretization of an underlying function, such as audio signals or time series. However, these models operate directly on the discretized data, and there are no semantics in the modeling process that relate the observed data to the underlying functional forms. We generalize diffusion models to operate directly in function space by developing the foundational theory for such models in terms of Gaussian measures on Hilbert spaces. A significant benefit of our function space point of view is that it allows us to explicitly specify the space of functions we are working in, leading us to develop methods for diffusion generative modeling in Sobolev spaces. Our approach allows us to perform both unconditional and conditional generation of function-valued data. We demonstrate our methods on several synthetic and real-world benchmarks.

Related papers

Synthetic location trajectory generation using categorical diffusion models [50.809683239937584]
Diffusion models (DPMs) have rapidly evolved to be one of the predominant generative models for the simulation of synthetic data. We propose using DPMs for the generation of synthetic individual location trajectories (ILTs) which are sequences of variables representing physical locations visited by individuals.
arXiv Detail & Related papers (2024-02-19T15:57:39Z)
Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformization [17.535229185525353]
We introduce an algorithm leveraging the uniformization of continuous Markov chains, implementing transitions on random time points. Our results align with state-of-the-art achievements for diffusion models in $mathbbRd$ and further underscore the advantages of discrete diffusion models in comparison to the $mathbbRd$ setting.
arXiv Detail & Related papers (2024-02-12T22:26:52Z)
Functional Diffusion [55.251174506648454]
We propose a new class of generative diffusion models, called functional diffusion. functional diffusion can be seen as an extension of classical diffusion models to an infinite-dimensional domain. We show generative results on complicated signed distance functions and deformation functions defined on 3D surfaces.
arXiv Detail & Related papers (2023-11-26T21:35:34Z)
Geometric Neural Diffusion Processes [55.891428654434634]
We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
arXiv Detail & Related papers (2023-07-11T16:51:38Z)
Functional Flow Matching [14.583771853250008]
We propose a function-space generative model that generalizes the recently-introduced Flow Matching model. Our method does not rely on likelihoods or simulations, making it well-suited to the function space setting. We demonstrate through experiments on several real-world benchmarks that our proposed FFM method outperforms several recently proposed function-space generative models.
arXiv Detail & Related papers (2023-05-26T19:07:47Z)
Infinite-Dimensional Diffusion Models [4.342241136871849]
We formulate diffusion-based generative models in infinite dimensions and apply them to the generative modeling of functions. We show that our formulations are well posed in the infinite-dimensional setting and provide dimension-independent distance bounds from the sample to the target measure. We also develop guidelines for the design of infinite-dimensional diffusion models.
arXiv Detail & Related papers (2023-02-20T18:00:38Z)
Score-based Diffusion Models in Function Space [140.792362459734]
Diffusion models have recently emerged as a powerful framework for generative modeling. We introduce a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space. We show that the corresponding discretized algorithm generates accurate samples at a fixed cost independent of the data resolution.
arXiv Detail & Related papers (2023-02-14T23:50:53Z)
Spectral Diffusion Processes [26.510979162244304]
Score-based generative modelling (SGM) has proven to be a very effective method for modelling densities on finite-dimensional spaces. We represent functional data in spectral space to dissociate part of the processes from their space-time part.
arXiv Detail & Related papers (2022-09-28T14:23:41Z)
A Survey on Generative Diffusion Model [75.93774014861978]
Diffusion models are an emerging class of deep generative models. They have certain limitations, including a time-consuming iterative generation process and confinement to high-dimensional Euclidean space. This survey presents a plethora of advanced techniques aimed at enhancing diffusion models.
arXiv Detail & Related papers (2022-09-06T16:56:21Z)
Generative Models as Distributions of Functions [72.2682083758999]
Generative models are typically trained on grid-like data such as images. In this paper, we abandon discretized grids and instead parameterize individual data points by continuous functions.
arXiv Detail & Related papers (2021-02-09T11:47:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.