Generative models have gained popularity for their potential applications in imaging science, such as image reconstruction, posterior sampling and data sharing. Flow-based generative models are particularly attractive due to their ability to tractably provide exact density estimates along with fast, inexpensive and diverse samples. Training such models, however, requires a large, high quality dataset of objects. In applications such as computed imaging, it is often difficult to acquire such data due to requirements such as long acquisition time or high radiation dose, while acquiring noisy or partially observed measurements of these objects is more feasible. In this work, we propose AmbientFlow, a framework for learning flow-based generative models directly from noisy and incomplete data. Using variational Bayesian methods, a novel framework for establishing flow-based generative models from noisy, incomplete data is proposed. Extensive numerical studies demonstrate the effectiveness of AmbientFlow in learning the object distribution. The utility of AmbientFlow in a downstream inference task of image reconstruction is demonstrated.

翻译：生成模型因其在成像科学中的潜在应用而受到关注，例如图像重建、后验采样和数据共享。基于流的生成模型尤为吸引人，因为它们能够以易于处理的方式提供精确的密度估计，并生成快速、廉价且多样化的样本。然而，训练此类模型需要大量高质量的物体数据集。在计算成像等应用中，由于需要长时间采集或高辐射剂量等原因，获取此类数据通常很困难，而获取这些物体的含噪或部分观测数据则更为可行。在这项工作中，我们提出了AmbientFlow，一个直接从含噪且不完整数据中学习基于流的生成模型的框架。利用变分贝叶斯方法，我们提出了一个从含噪、不完整数据中构建基于流的生成模型的新框架。大量数值研究表明了AmbientFlow在学习物体分布方面的有效性。同时，还展示了AmbientFlow在图像重建的下游推理任务中的实用性。