SPECULATIVE CORRECTION: DRAFT-THEN-REFINE DECODING FOR DIFFUSION LANGUAGE MODELS

Diffusion language models (DLMs) can revise tokens bidirectionally, but standard decoding procedures often adapt them to left-to-right generation by producing text block by block. We show that existing pretrained DLMs can directly refine previously completed block-autoregressive responses, without additional training or architectural modification. This yields a simple draft-then-refine decoding pattern: a model first generates a complete response, then treats that response as an editable initialization for bidirectional refinement. We study both same-model correction, where one checkpoint drafts and refines, and small-to-large speculative correction, where separately released small and large checkpoints are composed without joint training or adaptation. Same-model correction improves the evaluated quality-latency trade-off: on a held-out GSM8K set, it raises accuracy from $0.789$ to $0.916$ with a $384$-token budget while running $1.10\times$ faster, and on MATH-768 it matches the Flash score of $0.540$ while running $1.52\times$ faster. Small-to-large correction retains much of the cheaper model's speed. On MATH-384, it scores $0.282$ rather than $0.292$ while running $2.32\times$ faster than Flash. On MBPP+, it raises the fraction of programs passing the expanded tests from $0.484$ to $0.621$ while running $1.15\times$ faster in standardized timing. Refinement is sparse: it changes only about five to six final tokens per response and fixes substantially more answers than it harms. Taken together, these results show that a completed response provides enough structure for a short refinement stage to make useful changes. Within this plug-and-play framework, same-model correction shows that an existing checkpoint can achieve a better quality-latency trade-off through decoding alone, while small-to-large correction can combine separately released checkpoints into a cascade that often adds an intermediate operating point between them. The success of this off-the-shelf cascade further motivates training small and large DLMs for complementary drafting and refinement roles as a dedicated architecture.