Block Diffusion Language Models (BD-LMs) support KV caching and flexible-length generation, but their native Single-Block Diffusion (SingleBD) inference leaves inter-block parallelism unused. We study Multi-Block Diffusion (MultiBD), where a running-set of consecutive blocks is refined concurrently. Existing teacher-forced BD-LMs observe only one noisy block conditioned on a clean prefix, while diffusion forcing exposes a long noisy suffix whose state distribution still differs from practical MultiBD inference. We bridge this gap with Multi-Block Diffusion Language Models (MBD-LMs), obtained by post-training BD-LMs using Multi-block Teacher Forcing (MultiTF). MultiTF trains on bounded noise-groups conditioned on clean prefixes, with heterogeneous slot-wise noise patterns that better match inference. An optimized Block Buffer further preserves prefix-cache reuse and static input shapes, translating inter-block parallelism into wall-clock acceleration. On math and code benchmarks, MBD-LLaDA2-Mini increases average Tokens Per Forward pass (TPF) from 3.47 to 6.19 while maintaining comparable accuracy (80.0% versus 81.0%). Combined with DMax, it reaches 9.34 TPF with a 1.02-point accuracy drop. Project Page: https://sjtu-deng-lab.github.io/mbd-lms