Train the Sampler You Run: Few-Step Masked Diffusion Language Models via Mixture-Likelihood Fine-Tuning

When a masked diffusion language model is sampled in a few parallel steps in a random order, the model actually run is a mixture over reveal plans, while cross-entropy training fits token conditionals rather than this mixture. We introduce mixture-likelihood fine-tuning (Mix-FT), which fine-tunes a pretrained model on an importance-weighted bound of its own sampler's likelihood, with no teacher and no change to the architecture or the sampler. On LLaDA-8B, a LoRA fine-tune for 0.002% of the pretraining compute writes better OpenWebText continuations than continued cross-entropy and Alpha diffusion given the same compute, at every tested step count. With half the model evaluations, 16 rather than 32 steps per block, its continuations score better than the original model's in every seed under three judges, with confidence-based decoding as well as random order, and under confidence-based decoding two blinded LLM raters from different model families prefer them in 69 and 71% of pairs. On a public 110M-parameter block diffusion model, Mix-FT takes under four T4-hours and beats continued cross-entropy, Alpha diffusion and SDTT distillation at 4, 8 and 16 steps per block, under two judges in every seed. Exact likelihoods on text8, with a control that weights every plan equally, attribute about three quarters of the likelihood gain over continued cross-entropy to weighting each plan by how well it explains the sequence.