Rewriting the ELBO Explainer for Diffusion Language Model Training

zmkzmkz · x · 2026-09-30

The author previously wrote an article teaching himself the evidence lower bound (ELBO) for diffusion language model training, then found parts of it misleading and rewrote it.

The key takeaway: diffusion language models typically maximize the ELBO — a lower bound on log-likelihood — rather than log-likelihood directly, because directly optimizing the likelihood is intractable in diffusion models. The writeup starts from basic probabilistic models (e.g. conditional distributions like p(major|student)) and moves to how language models assign probabilities to text sequences, explaining step by step why the ELBO sidesteps the intractability. The author notes it is not a rigorous mathematical article and intentionally omits some details for clarity.

Original post →

More from Research

Research channel →