On Memorization in Probabilistic Deep Generative Models

In the last few years there have been incredible successes in generative modeling through the development of deep learning techniques such as variational autoencoders (VAEs) [1, 2], generative adversarial networks (GANs) [3], normalizing flows [4, 5], and diffusion networks [6], among others. The goal of generative modeling is to learn the data distribution of a given data set, which has numerous applications such as creating realistic synthetic data, correcting data corruption, and detecting anomalies. Novel architectures for generative modeling are typically evaluated on how well a complex, high dimensional data distribution can be learned by the model and how realistic the samples from the model are. An important question in the evaluation of generative models is to what extent observations from the training data are memorized by the learning algorithm. A common technique to assess memorization in deep generative models is to look for nearest neighbors. Typically, several samples are drawn from a trained model and compared to their nearest neighbors in the training set. There are several problems with this approach. First, it has been well established that when using the Euclidean metric this test can be easily fooled by taking an image from the training set and shifting it by a few pixels [7]. For this reason, nearest neighbors in the feature space of a secondary model are sometimes used, as well as cropping and/or downsampling before identifying nearest neighbors (e.g.