arXiv：cs.LG· Rodrigo Casado Noguerales, Bernhard Sch\"olkopf, Thomas Hofmann, Aran Raoufi·· 3 小时前
离散扩散模型究竟学到了什么？同一逆过程的三种坐标表示
What Does a Discrete Diffusion Model Learn? One Reverse Process in Three Coordinates
AI 导读
该研究证明离散扩散模型的去噪器、bridge plug-in 与具体分数只是同一逆过程的三种坐标表示，并给出它们之间的精确换算关系，纠正了 bridge plug-in 学习的是 cavity 分布而非去噪器的常见理解。
正文
Abstract: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 denoiser, bridge plug-in, and concrete score are three coordinates of this reverse process, derive exact conversions between them, and identify the probability distribution learned by each. In particular, contrary to its standard interpretation, the bridge plug-in learns not a denoiser but the cavity distribution: the clean token given the noisy sequence excluding its own position. We confirm the theory by training all three coordinates with masked, uniform, and GIDD kernels on OpenWebText under a shared recipe, and by training uniform-diffusion solvers on four logic tasks. The learned coordinates agree after conversion, while confusing the cavity with the denoiser can severely degrade sampling quality. Together with exact boundary-term formulas, closed-form NELBO calibrations at initialization, and a clock interpretation of time schedules, these results provide a conceptual framework and a mechanical recipe for deriving, implementing, and comparing discrete diffusion processes.
| Comments: | 48 pages, 10 figures. v2: revised and extended; accepted as an oral at the NeurIPS 2026 workshop Diffusion Language Models: Foundations, Efficiency, and Reasoning |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Information Theory (cs.IT); Machine Learning (stat.ML) |
| Cite as: | arXiv:2607.05381 [cs.LG] |
| (or arXiv:2607.05381v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.05381 arXiv-issued DOI via DataCite |
Submission history
From: Rodrigo Casado Noguerales [view email]
[v1]
Mon, 6 Jul 2026 17:56:11 UTC (257 KB)
[v2]
Wed, 14 Oct 2026 17:57:33 UTC (321 KB)
来源：arXiv：cs.LG · arxiv.org