Rethinking VAE: From Continuous to Discrete Representations Without Probabilistic Assumptions

This paper explores the generative capabilities of Autoencoders (AEs) and establishes connections between Variational Autoencoders (VAEs) and Vector Quantized-Variational Autoencoders (VQ-VAEs) through a reformulated training framework. We demonstrate that AEs exhibit generative potential via latent space interpolation and perturbation, albeit limited by undefined regions in the encoding space. To address this, we propose a new VAE-like training method that introduces clustering centers to enhance data compactness and ensure well-defined latent spaces without relying on traditional KL divergence or reparameterization techniques. Experimental results on MNIST, CelebA, and FashionMNIST datasets show smooth interpolative transitions, though blurriness persists. Extending this approach to multiple learnable vectors, we observe a natural progression toward a VQ-VAE-like model in continuous space. However, when the encoder outputs multiple vectors, the model degenerates into a discrete Autoencoder (VQ-AE), which combines image fragments without learning semantic representations. Our findings highlight the critical role of encoding space compactness and dispersion in generative modeling and provide insights into the intrinsic connections between VAEs and VQ-VAEs, offering a new perspective on their design and limitations.