What Does a Discrete Diffusion Model Learn? One Reverse Process in Three Coordinates
What does a discrete diffusion model actually learn? The literature trains denoisers, bridge plug-ins, and concrete scores, each deriving its own ELBO objective under different conventions. This fragmentation makes the object being learned unclear and ELBO values difficult to interpret and compare. All three methods learn the same object in different coordinates: the exact time-reversal of the noising process. We first prove the Oracle Distance identity: for any noising process, the negative ELBO is not just a bound on the likelihood; it equals the data entropy plus the path KL divergence from the reversed noising process to the learned one. Next, for token-factorizing noise, we show that...
| Authors | Rodrigo Casado Noguerales, Bernhard Schölkopf, Thomas Hofmann et al. |
|---|---|
| Primary category | cs.LG |
| Published | 6 July 2026 |
| Last updated at source | 14 October 2026 |
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