Latent-Plan Block Diffusion: Sampling a Block-Level Intent for Few-Step Parallel Decoding

Block diffusion language models such as BD3-LM use a masked-diffusion denoiser to decode a block of $B$ tokens in parallel while keeping the key–value (KV) cache of autoregressive models, but every denoising step samples the block from a product of per-token marginals. We show that the least error of drawing a block in one such step is its conditional total correlation given the context, a cost that unmasking schedules can only trade for more steps. *Latent-Plan Block Diffusion* (LP-BD) supplies the missing shared variable: before a block is decoded, a small conditional flow samples a low-dimensional *plan* given the generated prefix, and the denoiser decodes the block conditioned on it. The plan is learned from the denoiser's own loss, without supervision, and LP-BD equals BD3-LM at initialization, so it can be added to a pretrained model. Trained from scratch on TinyStories with 16-token blocks, LP-BD lowers the negative log-likelihood of one-step samples under an autoregressive judge by 31% and reaches 16-step BD3-LM quality with 8 steps. The gains are similar at 28M and 85M parameters. Added to the released 170M BD3-LM checkpoints on OpenWebText, LP-BD lowers generative perplexity at matched entropy by 14–55% at every step budget of a fixed-step sampler, and by 38–66% with guidance. The plan acts as a sampled *intent* shared by the block rather than a prediction from the context, and its gains require steps that decode several tokens jointly.