KL Divergence Between Gaussians: A Step-by-Step Derivation for the Variational Autoencoder Objective
Kullback-Leibler (KL) divergence is a fundamental concept in information theory that quantifies the discrepancy between two probability distributions. In the context of Variational Autoencoders (VAEs), it serves as a central regularization term, imposing structure on the latent space and thereby enabling the model to exhibit generative capabilities. In this work, we present a detailed derivation of the closed-form expression for the KL divergence between Gaussian distributions, a case of particular importance in practical VAE implementations. Starting from the general definition for continuous random variables, we derive the expression for the univariate case and extend it to the multivar...
| Authors | Andrés Muñoz, Rodrigo Ramele |
|---|---|
| Primary category | cs.LG |
| Published | 13 April 2026 |
| Last updated at source | 13 April 2026 |
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