Dependency-Aware Parallel Decoding via Attention for Diffusion LLMs

Parallel decoding for diffusion LLMs (dLLMs) is difficult because each denoising step provides only token-wise marginal distributions, while unmasking multiple tokens simultaneously requires accounting for inter-token dependencies. We propose Dependency-Aware Parallel Decoding (DAPD), a simple, training-free decoding method that uses self-attention to induce a conditional dependency graph over masked tokens. At each iteration, edges in this graph capture strong token interactions, while non-edges indicate weak dependence. Parallel decoding is then reduced to selecting an independent set on the graph and unmasking the selected tokens in parallel. This avoids co-updating strongly coupled tokens without auxiliary models or retraining. Experiments on LLaDA and Dream show that DAPD improves the accuracy-steps trade-off over existing methods and enables more globally distributed parallel updates that better exploit the any-order generation capability of dLLMs.

Understanding the Reversal Curse Mitigation in Masked Diffusion Models through Attention and Training Dynamics

Autoregressive language models (ARMs) suffer from the reversal curse: after learning that "$A$ is $B$", they often fail on the reverse query "$B$ is $A$". Masked diffusion-based language models (MDMs) exhibit this failure in a much weaker form, but the underlying reason has remained unclear. A common explanation attributes this mitigation to the any-order training objective. However, observing "[MASK] is $B$" during training does not necessarily teach the model to handle the reverse prompt "$B$ is [MASK]". We show that the mitigation arises from architectural structure and its interaction with training. In a one-layer Transformer encoder, weight sharing couples the two directions by making forward and reverse attention scores positively correlated. In the same setting, we further show that the corresponding gradients are aligned, so minimizing the forward loss also reduces the reverse loss. Experiments on both controlled toy tasks and large-scale diffusion language models support these mechanisms, explaining why MDMs partially overcome a failure mode that persists in strong ARMs.

Preserve-Then-Quantize: Balancing Rank Budgets for Quantization Error Reconstruction in LLMs

Quantization Error Reconstruction (QER) reduces accuracy loss in Post-Training Quantization (PTQ) by approximating weights as $\mathbf{W} \approx \mathbf{Q} + \mathbf{L}\mathbf{R}$, using a rank-$r$ correction to reconstruct quantization error. Prior methods devote the full rank budget to error reconstruction, which is suboptimal when $\mathbf{W}$ has intrinsic low-rank structure and quantization corrupts dominant directions. We propose Structured Residual Reconstruction (SRR), a rank-allocation framework that preserves the top-$k$ singular subspace of the activation-scaled weight before quantization, quantizes only the residual, and uses the remaining rank $r-k$ for error reconstruction. We derive a theory-guided criterion for selecting $k$ by balancing quantization-exposed energy and unrecoverable error under rank constraints. We further show that resulting $\mathbf{Q} + \mathbf{L}\mathbf{R}$ parameterization naturally supports Quantized Parameter-Efficient Fine-Tuning (QPEFT), and stabilizes fine-tuning via gradient scaling along preserved directions. Experiments demonstrate consistent perplexity reductions across diverse models and quantization settings in PTQ, along with a 5.9 percentage-point average gain on GLUE under 2-bit QPEFT.