d-OPSD: First on-policy self-distillation framework tailored for diffusion LLMs
Researchers introduce d-OPSD, the first on-policy self-distillation (OPSD) framework designed specifically for diffusion large language models (dLLMs). The method addresses a fundamental mismatch between existing autoregressive OPSD approaches and dLLMs' arbitrary-order generation by using suffix conditioning on self-generated answers and step-level rather than token-level divergence supervision. Across four reasoning benchmarks, d-OPSD outperforms RLVR and SFT baselines while requiring only ~10% of the optimization steps of RLVR, suggesting strong sample efficiency gains for dLLM post-training.
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Self-Policy Distillation via Capability-Selective Subspace Projection
This paper introduces Self-Policy Distillation (SPD), a self-distillation method for LLMs that requires no external signals such as correctness filters or reward models. SPD extracts a low-rank capability subspace from the model's own gradients on correctness-defining tokens, then projects KV activations into this subspace during self-generation to isolate task-relevant signal from stylistic noise. Experiments across code generation, math reasoning, and QA show up to 13% improvement over prior signal-free self-distillation methods and 15% better out-of-domain generalization.
OPCoD: On-Policy Co-Distillation for Mutual LLM Improvement via Peer Feedback
Researchers introduce On-Policy Co-Distillation (OPCoD), a training framework where two LLMs, each stronger in a different domain, iteratively tutor each other using on-policy rollouts and peer feedback. The method uses cognizance-based gating to control when feedback is given and feedback anchoring to ground it in the problem context. On Science Q&A tasks, OPCoD achieves Pareto improvement for both models across all evaluated domain pairs, outperforming one-way distillation and single-model fine-tuning baselines.
SARDI: Self-Augmenting Retrieval for Diffusion Language Models using lookahead tokens
Researchers introduce SARDI, a training-free RAG framework for discrete diffusion language models that repurposes discarded low-confidence tokens during denoising as lookahead signals to guide retrieval before output is finalized. The method is retriever-agnostic and applicable to any reasoning-capable discrete diffusion LM. Evaluated across five multi-hop QA benchmarks, SARDI outperforms training-free diffusion and autoregressive retrieval baselines at up to 8x higher throughput.
Vision-OPD: On-Policy Self-Distillation for Fine-Grained Visual Understanding in MLLMs
Vision-OPD addresses a 'regional-to-global perception gap' in multimodal LLMs, where models answer fine-grained visual questions more accurately when given cropped evidence regions than full images. The method instantiates a crop-conditioned teacher and full-image-conditioned student from the same MLLM, minimizing token-level divergence along on-policy rollouts to transfer regional perception to the full-image policy. This self-distillation requires no external teacher models, ground-truth labels, reward verifiers, or inference-time tools. Benchmarks show competitive or superior performance against larger open-source, closed-source, and agentic 'Thinking-with-Images' models.
Diffusion-Proof: First framework applying diffusion LLMs to formal theorem proving
Researchers introduce Diffusion-Proof, the first framework to train and apply diffusion language models (dLLMs) for formal theorem proving, addressing limitations of autoregressive models in long-range coherence. The framework includes dLLM-Prover-7B for whole-proof generation and dLLM-Corrector-7B for local proof correction via bidirectional infilling. Diffusion-Proof achieves absolute improvements of 1.61% on ProofNet-Test and 6.14% on MiniF2F-Test over an AR baseline, and solves one IMO problem that DeepSeek-Prover-V2-7B could not. The result suggests dLLMs may have structural advantages over AR models for tasks requiring long-range logical coherence.
Skill-Conditioned Gated Self-Distillation (SGSD) for LLM Reasoning
SGSD is a new on-policy self-distillation method for LLM reasoning that replaces trusted privileged information (e.g., reference answers) with an experience-derived skill bank of skill-mistake pairs. It constructs a multi-teacher pool, validates each teacher's contribution via a verifier, and applies a gated objective to distill informative disagreements while suppressing noisy signals. On Qwen3-1.7B, SGSD outperforms GRPO by 6.2% and answer-conditioned OPSD by 1.7% on average across AIME24, AIME25, and HMMT25. The method relaxes the assumption of trusted privileged information, making self-distillation more practical under weaker supervision.
RePlaid: Continuous Diffusion Language Models Scale Competitively with Discrete Diffusion
This paper revisits continuous diffusion language models (DLMs) by introducing RePlaid, an updated version of Plaid that aligns its architecture with modern discrete DLMs. RePlaid establishes the first scaling law for continuous DLMs competitive with discrete approaches, achieving a compute gap of only 20× versus autoregressive models and a state-of-the-art perplexity bound of 22.1 on OpenWebText among continuous DLMs. The authors provide theoretical analysis showing that likelihood-based training naturally yields linear cross-entropy over time and creates structured embedding geometries, explaining the performance gains.
SDXL in 4 Steps with Latent Consistency LoRAs
Hugging Face demonstrates combining Latent Consistency Models (LCMs) with LoRA adapters to enable high-quality image generation with Stable Diffusion XL in as few as 4 inference steps. This approach dramatically reduces the number of diffusion steps required compared to standard SDXL, lowering inference latency and compute cost. The technique leverages consistency distillation applied via lightweight LoRA weights, making it accessible without full model retraining.