ForkLeft: Entropy-First Rollouts for Prefix-Aligned Autoregressive-to-Diffusion Distillation

On-policy distillation (OPD) is a post-training approach for large language models (LLMs) that enables a student model to learn a teacher model's distribution from sequences sampled from the student's own policy. Despite its promising capability, OPD for diffusion language models (DLMs) remains underexplored and existing studies primarily focuses on DLM-to-DLM distillation. The limited availability of strong teacher DLMs and the flexible generation order of DLMs impose additional technical challenges as well. However, it remains unclear how to effectively distill knowledge from a strong autoregressive language model (ARM) into a weaker DLM, given the mismatch between the left-to-right decoding of ARMs and the flexible decoding order of DLMs. Inspired by Ni et al. (2026), we propose JustOPD, an ARM-to-DLM on-policy distillation method that uses autoregressive rollouts during training to align the student's generation process with the ARM teacher's left-to-right decoding. This alignment enables effective distillation from ARM teachers while preserving the DLM's flexible generation-order capability at inference time. Experiments using Qwen3-14B as the teacher and Dream-7B as the student demonstrate that JustOPD consistently improves mathematical reasoning performance over the base DLM across multiple divergence choices.

We study the transformation of autoregressive models (ARLMs) into diffusion language models (DLMs). Rather than pretraining from scratch, prior work replaces the causal attention in ARLMs with bidirectional attention and then trains the resulting model using a DLM objective. However, these approaches incur two distribution shifts. First, transitioning from a next-token prediction objective to a DLM objective can discard knowledge acquired by the ARLM during training. Second, standard DLMs suffer from a train-inference mismatch, as the training loss is defined on randomly masked sequences rather than the trajectories encountered at inference produced by confidence-based decoding. To address both challenges, we introduce an On-Policy Diffusion Language Model (OPDLM) in which On-Policy Distillation (OPD) is employed for ARLM-to-DLM transformation. Specifically, OPDLM is trained via self-OPD, where the student, an ARLM with bidirectional attention, generates its own trajectories, and the teacher, the original frozen ARLM, distills its knowledge by providing target logits on these trajectories. By training directly in an on-policy manner, OPDLM eliminates the train-inference mismatch in DLMs, while distillation from the original model enhances knowledge retention from the ARLM. Empirical results demonstrate that OPDLM requires 15x to 7,000x fewer training tokens with strong performance across a wide variety of tasks. OPDLM avoids the prohibitive cost of DLM pretraining and positions DLM transformation as a form of ARLM post-training.

Diffusion Language Models (DLMs) are often advertised as enabling parallel token generation, yet practical fast DLMs frequently converge to left-to-right, autoregressive (AR)-like decoding dynamics. In contrast, genuinely non-AR generation is promising because it removes AR's sequential bottleneck, better exploiting parallel hardware to reduce synchronization/communication overhead and improve latency scaling with output length. We argue that a primary driver of AR-like decoding is a mismatch between DLM objectives and the highly sequential structure of widely used training data, including standard pretraining corpora and long chain-of-thought (CoT) supervision. Motivated by this diagnosis, we propose NAP (Non-Autoregressive Parallel DLMs), a proof-of-concept, data-centric approach that better aligns supervision with non-AR parallel decoding. NAP curates examples as multiple independent reasoning trajectories and couples them with a parallel-forced decoding strategy that encourages multi-token parallel updates. Across math reasoning benchmarks, NAP yields stronger performance under parallel decoding than DLMs trained on standard long CoT data, with gains growing as parallelism increases. Our results suggest that revisiting data and supervision is a principled direction for mitigating AR-like behavior and moving toward genuinely non-autoregressive parallel generation in DLMs. Our code is available at https://github.com/pixeli99/NAP.