Speculative decoding is used to reduce the inference cost of language models. One-step diffusion drafters propose a block of multiple tokens in parallel, reducing the sequential cost of speculative decoding. On-policy distillation trains these drafters using verifier feedback on their own proposals. However, parallel drafting makes this feedback difficult to use: the drafter predicts each token without observing the preceding tokens sampled within the same block, while the verifier conditions its prediction on those tokens. Different sampled prefixes therefore give different verifier targets for the same drafter prediction. We show that distilling against these targets separately can suppress tokens that are plausible after some prefixes but unlikely after others, harming draft acceptance. We explain the effects of this mismatch and introduce Multi-Draft On-Policy Distillation (MDraft), a new parallel drafter distillation method which samples several draft blocks from the same context and aggregates the verifier's full-vocabulary conditionals across their prefixes. We use all the drafts to collect information from the verifier, allowing support from alternative prefixes to influence the training target. The resulting algorithm improves the acceptance length of a parallel drafter beyond the level of pre-training, and alleviates the effects of the distributional mismatch. MDraft changes only training, retaining the drafter's architecture and inference procedure, allowing the resulting drafter to be used as-is in place of the pretrained checkpoint. Experiments on a suite of mathematical, coding, and conversational tasks show longer accepted drafts than prior distillation methods.

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