## 1 Introduction  
A breakthrough in creating powerful generative models has been the invention of Generative Adversarial Networks (GANs) [1]. In principle, GANs are capable of modelling any high dimensional data distribution through the training of two adversarial neural networks. The networks are trained together in a competing manner: one network generates data whose distribution approximates the distribution of the real data; hence, it is called the generator, while the other neural network evaluates whether the generated data are real or not; hence, it is called the discriminator. GANs have been proven very successful in generating photo-realistic images and audio/speech samples. Applications of GANs include (conditional) image generation [2; 3; 4; 5; 6; 7; 8], image-to-image translation [9] and image super-resolution [10]. In time-series, GANs have been used for speech enhancement [11] and speech synthesis [12; 13] as well as for natural language processing [14; 15] among other types of raw data. More recently, they have been started to show their usefulness in life science applications [16], too. GANs often face training difficulties when applied in single-cell data; either gene expression or proteomic data. The main reason is that cells constantly shift from one state or type to another, either naturally like in an immune response or artificially like after a drug treatment, and the current sequencing technology allows only sparse observations scattered along the evolution of the samples [17]. For example, single-cell RNA sequencing (scRNAseq) is able to capture the diversity of cells during cell differentiation or activation by profiling transcript abundances at high resolution. However, it does so by creating snapshot observations where the temporal resolution is low or totally unknown. Consequently, some cell states may be missing entirely or a low number of samples are available from those states [18]. On top of that, the collected data include a huge amount of zero values (i.e., element-wise zero-inflated samples) that cause established analysis methods to break down [19]. In scRNAseq modeling, representation and generation, GANs and more generally generative models have been utilized for imputing missing values in the data, for dimensionality reduction, for mapping data across different measurement types (e.g., domain adaptation), for data augmentation through the approximation of the original data distribution and for modeling the response of differentiating cells upon external perturbation. Particularly, an early work on GANs with scRNAseq data was the identification of state-determining genes and clustering tasks [20]. [PERSON] et al. [21] developed a conditional GAN for data augmentation of single-cell data sets demonstrating realistic in-silico generation of low size cell types. In [22], authors took into account the zero-inflation of the data and proposed a variational autoencoder for clustering purposes. On a different approach to mitigate the excess amount of zeros in the expression matrix, authors in [23; 24] performed data imputation. In [23], particularly, the authors converted scRNAseq data to images and then trained GANs to perform dropout imputation and related downstream analysis. Here, we build on the existing literature and further present:  
1. Semi-interpretable generators that generate synthetic data that follow the statistical properties of biological data and particularly the mixed nature of the distributions of single-cell RNA-seq expression data. 2. Based on the framework of GANs, a novel training approach for a mixture model of zero-inflated multi-dimensional variables. We utilize Renyi divergence minimization for the first time on biological data to estimate the parameters. Overall, the proposed approach is more flexible since it does not require the optimization over an (assumed) likelihood function. 3. Comparisons between neural network generators (not interpretable) and the proposed semi-interpretable generators for data interpolation and data augmentation tasks.