Abstract: Diffusion drafters accelerate speculative decoding by proposing multiple tokens in parallel. Despite recent advances in speculative decoding through sequence-level drafting and verification, existing training objectives remain largely designed around token-level verification. To address this mismatch, we introduce Block Verification-aware loss (BV loss), a training objective designed to maximize the expected acceptance length of a drafted sequence. BV loss is directly derived from the block verification acceptance rule, providing a principled connection between the drafter training objective and the inference-time verification mechanism at the sequence level. Across math, code, and chat benchmarks, BV loss increases the mean number of tokens accepted per verification call under block verification by 13.0--21.0\% over cross-entropy loss training for DFlash and DSpark with Qwen3-4B and Qwen3-8B without changing the inference procedure. BV loss also outperforms tokenwise acceptance objectives such as TV loss and LK loss, and its gains extend to token verification and greedy decoding. These results demonstrate the benefit of training block diffusion drafters with an objective aligned with sequence-level verification, rather than optimizing each token independently.