Recovering Control from Compact Codes: Residual Control in Diffusion Language Models

A compact condition can remain semantically informative while losing its influence on generation. We study this representation–use gap in an embedding-space diffusion language model. Under severe compression on TinyStories ($k=16$), direct conditioning loses control of one to three of six reliably encoded attributes across three seeds. Interventions that strengthen the denoiser's response to the same code recover control without increasing code dimension, implicating effective code–denoiser coupling as the bottleneck. Residual training provides a practical realization: it preserves all six TinyStories attributes and improves control on BeerAdvocate. Neutral-code guidance and Feynman–Kac particle steering improve both direct and residual models, while the residual model retains stronger control under matched controller settings. This shows that residual training can be combined with inference-time control to further strengthen controllability. The same residual-target intervention does not reliably improve an ELF flow model, establishing a generator-family boundary. These findings distinguish what a compact code represents from how effectively a generator uses it, and identify residual training as a targeted remedy for conditioning under-use.