Sampling From Autoencoders' Latent Space via Quantization And
  Probability Mass Function Concepts
Aymene Mohammed Bouayed Adrian Iaccovelli David Naccache
In this study, we focus on sampling from the latent space of generative
models built upon autoencoders so as the reconstructed samples are lifelike
images. To do to, we introduce a novel post-training sampling algorithm rooted
in the concept of probability mass functions, coupled with a quantization
process. Our proposed algorithm establishes a vicinity around each latent
vector from the input data and then proceeds to draw samples from these defined
neighborhoods. This strategic approach ensures that the sampled latent vectors
predominantly inhabit high-probability regions, which, in turn, can be
effectively transformed into authentic real-world images. A noteworthy point of
comparison for our sampling algorithm is the sampling technique based on
Gaussian mixture models (GMM), owing to its inherent capability to represent
clusters. Remarkably, we manage to improve the time complexity from the
previous $\mathcal{O}(n\times d \times k \times i)$ associated with GMM
sampling to a much more streamlined $\mathcal{O}(n\times d)$, thereby resulting
in 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 diverse
range of models and datasets. On the MNIST benchmark dataset, our approach
outperforms GMM sampling by yielding a noteworthy improvement of up to $0.89$
in FID value. Furthermore, when it comes to generating images of faces and
ocular images, our approach showcases substantial enhancements with FID
improvements of $1.69$ and $0.87$ respectively, as compared to GMM sampling, as
evidenced on the CelebA and MOBIUS datasets. Lastly, we substantiate our
methodology's efficacy in estimating latent space distributions in contrast to
GMM sampling, particularly through the lens of the Wasserstein distance.