Generative models have proven to be an outstanding tool for representing high-dimensional probability distributions and generating realistic looking images. A fundamental characteristic of generative models is their ability to produce multi-modal outputs. However, while training, they are often susceptible to mode collapse, which means that the model is limited in mapping the input noise to only a few modes of the true data distribution. In this paper, we draw inspiration from Determinantal Point Process (DPP) to devise a generative model that alleviates mode collapse while producing higher quality samples. DPP is an elegant probabilistic measure used to model negative correlations within a subset and hence quantify its diversity. We use DPP kernel to model the diversity in real data as well as in synthetic data. Then, we devise a generation penalty term that encourages the generator to synthesize data with a similar diversity to real data. In contrast to previous state-of-the-art generative models that tend to use additional trainable parameters or complex training paradigms, our method does not change the original training scheme. Embedded in an adversarial training and variational autoencoder, our  Generative DPP approach shows a consistent resistance to mode-collapse on a wide-variety of synthetic data and natural image datasets including MNIST, CIFAR10, and CelebA, while outperforming state-of-the-art methods for data-efficiency, convergence-time, and generation quality. Our code will be made publicly available. Deep generative models have gained enormous research interest in recent years as a powerful framework to learn high dimensional data in an unsupervised fashion. Generative Adversarial Networks (GANs) BID10 and Variational AutoEncoders (VAEs) are among the most dominant generative approaches. They consist of training two networks: a generator (decoder) and a discriminator (encoder), where the generator attempts to map random noise to fake data points that simulate the probability distribution of real data. . GANs are typically associated with higher quality images compared to VAEs. Nevertheless, in the process of learning multi-modal complex distributions, both models may converge to a trivial solution where the generator learns to produce few modes exclusively, as referred to by mode collapse problem.To address this, we propose utilizing Determinantal Point Processes (DPP) to model the diversity within data samples. DPP is a probabilistic model that has been mainly adopted for solving subset selection problems with diversity constraints BID21 , such as video and document summarization. However, Sampling from a DPP requires quantifying the diversity of 2 N subsets, where N is the size of the ground set. This renders DPP sampling from true data to be computationally inefficient in the generation domain. The key idea of our work is to model the diversity within real and fake data throughout the training process, which does adds an insignificant computational cost. Then, We encourage producing samples of similar diversity distribution to the true-data by back-propagating the DPP metric through the generator. This way, generator explicitly learns to cover more modes of real distribution, and accordingly alleviates mode collapse.Recent approaches tackled mode-collapse in one of two different ways: (1) improving the learning of the system to reach a better convergence point(e.g. BID28 ; BID0 ); or (2) explicitly enforcing the models to capture diverse modes or map back to the true-data distribution (e.g. BID37 ; BID2 ). Here we focus on a relaxed version of the former, where we use the same learning paradigm of the standard GANs and only change the objective function. The advantage of such an approach is to avoid adding any extra trainable parameters to the trained system while maintaining the same back-propagation steps as the standard GANs. Thus, our model converges faster to a fair equilibrium point where the generator captures the diversity of the true-data distribution while preserving the quality of generations.Contribution. We introduce a new loss function, that we denote Generative Determinantal Point Processes (GDPP) loss. Our loss only assumes an access to a generator G, a feature extraction function φ(·), and sampler from true data distribution p d . The loss encourages the generator to diversify generated samples that match the diversity of real data.This criterion can be considered as a complement to the original adversarial loss which attempts to learn an indistinguishable distribution from the true-data distribution without being specific to diverse modes. We assess the performance of GDPP on three different synthetic data environments, while also verifying the superiority on three real-world images datasets. We compared our approach with state-of-the-art approaches of more complex architectures and learning paradigms. Experiments show that our method outperforms all competing methods in terms of alleviating modecollapse and generations quality. In this work, we introduce a novel criterion to train generative networks on capturing a similar diversity to one of the true data by utilizing Determinantal Point Process(DPP). We apply our criterion to Generative Adversarial training and the Variational Autoencoder by learning a kernel via features extracted from the discriminator/encoder. We train the generator on optimizing a loss between the fake and real, eigenvalues and eigenvectors of this kernel to simulate the diversity of the real data. Our GDPP framework accumulates many desirable properties: it does not require any extra trainable parameters, it operates in an unsupervised setting, yet it consistently outperforms stateof-the-art methods on a battery of synthetic data and real image datasets as measure by generation quality and invariance to mode collapse. Furthermore, GDPP-GANs exhibit a stabilized adversarial training and has been shown to be time and data efficient as compared to state-of-the-art approaches. Moreover, the GDPP criterion is architecture and model invariant, allowing it to be embedded with any variants of generative models such as adversarial feature learning or conditional GANs.
The addition of a diversity criterion inspired from DPP in the GAN objective avoids mode collapse and leads to better generations. 
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