ELBO explained in one diagram: how VAEs trade reconstruction against regularization
cneuralnetwork · x · 2026-11-12
A single-diagram explanation of the ELBO in variational autoencoders.
- VAEs want to maximize log p(x), but the marginal likelihood is intractable, so we instead maximize the lower bound: ELBO = Eq(z|x)[log p(x|z)] − KL(q(z|x) || p(z)).
- Two competing objectives: reconstruction maximizes expected log-likelihood (make reconstructions x̂ close to the true x), while regularization minimizes the KL divergence between the approximate posterior q(z|x) and the prior p(z), e.g. N(0,I).
- Since log p(x) ≥ ELBO, maximizing ELBO yields a tractable objective for training generative models.
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