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In this study, we focus on sampling from the latent space of generativemodels built upon autoencoders so as the reconstructed samples are lifelikeimages. To do to, we introduce a novel post-training sampling algorithm rootedin the concept of probability mass functions, coupled with a quantizationprocess. Our proposed algorithm establishes a vicinity around each latentvector from the input data and then proceeds to draw samples from these definedneighborhoods. This strategic approach ensures that the sampled latent vectorspredominantly inhabit high-probability regions, which, in turn, can beeffectively transformed into authentic real-world images. A noteworthy point ofcomparison for our sampling algorithm is the sampling technique based onGaussian mixture models (GMM), owing to its inherent capability to representclusters. Remarkably, we manage to improve the time complexity from theprevious $\mathcal{O}(n\times d \times k \times i)$ associated with GMMsampling to a much more streamlined $\mathcal{O}(n\times d)$, thereby resultingin substantial speedup during runtime. Moreover, our experimental results,gauged through the Fr\'echet inception distance (FID) for image generation,underscore the superior performance of our sampling algorithm across a diverserange of models and datasets. On the MNIST benchmark dataset, our approachoutperforms GMM sampling by yielding a noteworthy improvement of up to $0.89$in FID value. Furthermore, when it comes to generating images of faces andocular images, our approach showcases substantial enhancements with FIDimprovements of $1.69$ and $0.87$ respectively, as compared to GMM sampling, asevidenced on the CelebA and MOBIUS datasets. Lastly, we substantiate ourmethodology's efficacy in estimating latent space distributions in contrast toGMM sampling, particularly through the lens of the Wasserstein distance.

Sampling From Autoencoders' Latent Space via Quantization And Probability Mass Function Concepts