Recent approaches build on implicit neural representations (INRs) to propose generative models over function spaces. However, they are computationally costly when dealing with inference tasks, such as missing data imputation, or directly cannot tackle them. In this work, we propose a novel deep generative model, named VAMoH. VAMoH combines the capabilities of modeling continuous functions using INRs and the inference capabilities of Variational Autoencoders (VAEs). In addition, VAMoH relies on a normalizing flow to define the prior, and a mixture of hypernetworks to parametrize the data log-likelihood. This gives VAMoH a high expressive capability and interpretability. Through experiments on a diverse range of data types, such as images, voxels, and climate data, we show that VAMoH can effectively learn rich distributions over continuous functions. Furthermore, it can perform inference-related tasks, such as conditional super-resolution generation and in-painting, as well or better than previous approaches, while being less computationally demanding.

翻译：近期研究基于隐式神经表示(INRs)提出了函数空间上的生成模型。然而,这些模型在处理缺失数据插补等推理任务时计算成本高昂,或者根本无法处理此类任务。本文提出一种新颖的深度生成模型——VAMoH。VAMoH结合了使用INRs建模连续函数的能力与变分自编码器(VAEs)的推理能力。此外,VAMoH采用归一化流定义先验分布,并利用超网络混合模型参数化数据对数似然,从而赋予VAMoH强大的表达能力和可解释性。通过在图像、体素和气候数据等多种数据类型上的实验,我们证明VAMoH能够有效学习连续函数上的丰富分布。同时,与现有方法相比,VAMoH能以更低计算成本完成条件超分辨率生成和图像修复等推理任务,性能持平或更优。