MIT 6.7960 L15: Variational Autoencoders (VAE) — ELBO, Reparameterization Trick, and Latent Representations
The core of VAE is ELBO + reparameterization: log p(x) is replaced with E_q[log p(x|z)] − KL(q(z|x)‖p(z)); the encoder outputs μ/σ and z = μ + σ⊙ε (ε ~ N(0,1)) makes sampling differentiable. Training = reconstruction + KL in tension, which gives rise to β-VAE, posterior collapse, VQ-VAE, and related fixes.