Recent approaches build on implicit neural representations (INRs) to propose generative models over function spaces. However, they are computationally intensive 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：近期方法基于隐式神经表示（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开销巨大，甚至完全无法处理此类任务。本文提出了一种名为VAMoH的新型深度生成模型。VAMoH结合了INRs对连续函数建模的能力与变分自编码器（VAEs）的推理能力。此外，VAMoH利用归一化流定义先验分布，并采用超网络混合模型参数化数据对数似然，从而赋予模型高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，它在条件超分辨率生成和图像修复等推理任务上的表现与已有方法相当或更优，且计算需求更低。