Branch-Jacobi: Prefix-Conditioned Multi-Pass Drafting for Speculative Decoding

Block-diffusion drafters predict token blocks in parallel, but later predictions cannot condition on tokens selected earlier in the same pass. We introduce Branch-Jacobi, which reuses one DFlash-style drafter for multi-pass prefix-conditioned refinement. Each pass packs prefix-MASK branches into one forward call. Consecutive first-MASK checks identify the proposal's common prefix with a drafter-autoregressive path; selecting one complete branch extends certification before linear target verification. We prove sound prefix certification for deterministic greedy drafting under fixed cycle conditions and equivalent branch evaluation. Moving-anchor training and causal prefix supervision align the drafter with variable-prefix queries. Across seven math, code, and chat benchmarks on Qwen3-4B and Qwen3-8B at temperatures 0 and 1, a three-layer drafter using three passes per cycle achieves $4.93$–$6.40\times$ geometric-mean decode-stage speedups over target autoregressive decoding, exceeding DFlash by $25.3$–$29.2\%$ while increasing average acceptance length.