When Top-1 Fails: Calibrating LoRA Monitors for Masked Diffusion LMs

Diffusion language models (DLMs) have recently emerged as competitive alternatives to autoregressive (AR) language models, yet differences in their activation dynamics remain poorly understood. We characterize these dynamics in LLaDA-8B and identify a striking layer-collapse property: a few early layers exhibit highly similar, collapsed activation patterns dominated by a single large super-outlier persisting over a long token range. Despite its apparent redundancy, this outlier is critical: pruning it causes outputs to degrade into repetitive random token loops. Paradoxically, layers in LLaDA contain more redundant representations overall, with redundancy most pronounced in earlier layers -- the reverse of AR models, where deeper layers grow redundant due to undertraining. Our analysis indicates that layer collapse in DLMs is not driven by undertraining but by overtraining: a dominant outlier becomes an indispensable information carrier while remaining representations collapse into redundant structure. These findings have strong practical implications, verified through controlled pre-training experiments. DLMs are surprisingly robust to compression: LLaDA under 3-bit GPTQ quantization drops only -1.8% on GSM8K, whereas Llama-3.1-8B drops -64.7%. Optimal sparsity allocation also reverses between families: at 50% average sparsity, allocating more to early layers in LLaDA yields +8.4% over the reverse strategy, while the same allocation costs Llama -8.4%. Our findings reveal that the DLM training objective fundamentally reshapes layer dynamics relative to AR models, with direct consequences for compression and deployment. Code: github.com/Conzel/super-outlier-dlm.

Frontier large language model training consumes massive accelerator fleets and long wall-clock computation, making stability failures costly when they occur. After a numerical or a hyperparameter fault has already destabilized the training dynamics, it may continue for thousands of steps while loss and gradient norms still appear normal. We study mechanism-driven detection of training instability by deriving internal monitors from the functional role of each critical module and from the earliest computational sites where failures are expected to produce measurable signatures. For low-precision flash attention, we monitor the spectral entropy of a QK bilinear decomposition, whose first-order term becomes abnormal before the loss fully collapses. For MoE routers, we derive indicators from their role in expert selection. Our fault-injection experiments on low-precision attention, large learning-rate, and combined faults show that these signals provide distinct signatures for different failures, triggering thousands of steps before loss divergence.

We aim to improve the reasoning capabilities of diffusion language models (DLMs). While SFT is a popular post-training recipe for autoregressive models, its use in DLMs faces challenges and can even hurt performance, though the underlying causes remain understudied. Our analysis reveals that vanilla SFT overlooks learnability, namely what and when tokens are learned. Specifically, rare tokens are difficult to learn when most of the input is masked, whereas it is straightforward and thus of little value to learn common tokens when most of the input is unmasked. Motivated by our analysis, we propose LIFT, an efficient SFT-based post-training algorithm for DLMs. LIFT learns easy tokens when most of the input is masked and hard tokens when more context is available, thus aligning the training with the information available at different diffusion time steps. Our results show that LIFT outperforms existing SFT baselines across six reasoning benchmarks, achieving up to a 3x relative gain on AIME'24 and AIME'25. Our code is publicly available at https://github.com/divelab/LIFT.