Variational autoencoders (VAEs)
Definition
VAEs learn a latent space by training an encoder-decoder with a variational (reparameterized) objective. They support generation and smooth interpolation in latent space.
They differ from GANs (adversarial) and diffusion (denoising): the latent space is regularized (KL to a prior) so it is smooth and interpretable. Generation can be blurrier than GANs/diffusion, but VAEs are useful for representation learning, anomaly detection, and when a low-D latent is desired.
How it works
Input is passed to an encoder that outputs parameters of a latent distribution (e.g. mean and log-variance for Gaussian). A z vector is sampled (reparameterization trick: z = mean + std * epsilon) and fed to the decoder, which reconstructs the input. Loss = reconstruction loss (e.g. MSE or cross-entropy) + KL divergence from the latent to a prior (e.g. standard normal). The KL term regularizes the latent space; the reconstruction term keeps it informative. At generation time, sample z from the prior and run the decoder.
Use cases
VAEs suit tasks that need a continuous latent space: smooth generation, anomaly detection, or learned representations.
- Generative modeling with smooth latent interpolation
- Anomaly detection via reconstruction error
- Learned representations for downstream tasks