HiLo-RD: Cross-Budget Self-Distillation for Masked Diffusion Language Models

We propose **HiLo-RD** (**Hi**gh-to-**Lo**w Budget **R**epresentation **D**istillation) to improve masked diffusion language models (MDLMs) under a limited generation budget. Unlike autoregressive models, MDLMs choose both what to generate and where to commit it. This creates two coupled challenges: predicting useful content before reasoning is complete, and deciding when to fix answer tokens that shape later predictions. We identify ***budget-induced premature commitment***: even when a correct solution fits, the model can fix answer fragments near the window boundary before resolving intermediate steps. These fragments become context for later predictions and redirect subsequent reasoning. Existing post-training methods do not directly transfer the stronger trajectories that the same model follows with a larger window. HiLo-RD addresses this gap by (1) pairing large-window teacher states with cropped small-window views and (2) matching their hidden representations at committed positions. This supervision guides both token prediction and commitment order without an external teacher. Across mathematics benchmarks, HiLo-RD improves low-budget accuracy and shortens responses; these gains extend to code generation without code-domain training. On GSM8K, accuracy rises by 9.4 percentage points as mean readable length falls by about 25%. Attention diagnostics and fixed-budget order interventions support the proposed mechanism. Together, these results show that large-window reasoning can improve small-window decoding.