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Trans-Dimensional Generative Modeling via Jump Diffusion Models

2023-05-25 17:15:00
Andrew Campbell, William Harvey, Christian Weilbach, Valentin De Bortoli, Tom Rainforth, Arnaud Doucet

Abstract

We propose a new class of generative models that naturally handle data of varying dimensionality by jointly modeling the state and dimension of each datapoint. The generative process is formulated as a jump diffusion process that makes jumps between different dimensional spaces. We first define a dimension destroying forward noising process, before deriving the dimension creating time-reversed generative process along with a novel evidence lower bound training objective for learning to approximate it. Simulating our learned approximation to the time-reversed generative process then provides an effective way of sampling data of varying dimensionality by jointly generating state values and dimensions. We demonstrate our approach on molecular and video datasets of varying dimensionality, reporting better compatibility with test-time diffusion guidance imputation tasks and improved interpolation capabilities versus fixed dimensional models that generate state values and dimensions separately.

Abstract (translated)

我们提出一种新的生成模型,该模型通过同时 Modeling 每个数据点的状态和维度,自然地处理不同维度的数据。生成过程可以表述为在不同维度空间中的跳跃扩散过程。我们首先定义一个破坏维度的向前噪声过程,然后推导出维度生成的逆生成过程,并提出了一种新的证据下的训练目标,以学习近似该逆生成过程。模拟我们学习到的近似逆生成过程,然后通过同时生成状态值和维度,有效地采样不同维度的数据。我们在不同维度的分子和视频数据集上演示了我们的这种方法,并报告了与测试时扩散指导插值任务更好的兼容性,以及与生成状态值和维度分别独立的固定维度模型相比,更好的插值能力。

URL

https://arxiv.org/abs/2305.16261

PDF

https://arxiv.org/pdf/2305.16261.pdf


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