Spherical Soft-Masking (S-SM), a drop-in replacement that aggregates the top-(k) predictions with a Fr'echet mean on the hypersphere and blends this mean with the mask direction using spherical linear interpolation (SLERP), then restores the native mask norm.
Abstract
Soft-masking accelerates the convergence of Masked Diffusion Language Models (MDLMs). Existing formulations build this blend with linear interpolation (LERP) in the raw embedding space, which implicitly treats that space as Euclidean. We analyze the embedding space of MDLMs and find that the mask and predicted-token embeddings maintain a near-constant angle of (\approx 73^\circ) throughout training, while embedding norms remain essentially flat across vocabulary-frequency rank. These indicate a hyperspherical geometry, for which LERP is the wrong interpolation primitive. We introduce Spherical Soft-Masking (S-SM), a drop-in replacement that aggregates the top-(k) predictions with a Fr'echet mean on the hypersphere and blends this mean with the mask direction using spherical linear interpolation (SLERP), then restores the native mask norm. We evaluate S-SM on continued pre-training of a released 169M-parameter MDLM checkpoint across a wide range of inference-time step budgets, SLERP feedback avoids the training degradation that LERP feedback induces and delivers MAUVE gains of up to 2x over the vanilla MDLM baseline and 27.5-56.1% over TopK/LERP at various sampling budgets, alongside consistently lower generative perplexity (16.9-19.6% over the baseline), while leaving output entropy and convergence essentially unchanged.
Masked diffusion language models (MDLMs) enable parallel generation and bidirectional context modeling, but their positional context differs fundamentally from that of autoregressive (AR) models. Whereas AR decoding exposes a contiguous prefix, MDLM denoising produces dynamic, non-contiguous configurations of revealed and masked tokens. Conventional positional encodings such as RoPE capture sequence order and pairwise displacement but remain insensitive to this evolving token-availability structure. To address this limitation, we propose MDLMPE, a positional encoding designed specifically for masked diffusion. To the best of our knowledge, MDLMPE is the first method to make positional representations explicitly aware of the changing revealed/masked configuration. It represents token availability as a binary sequence, applies distance-aware Gaussian weighting, and projects the resulting pattern through a cosine basis to obtain distribution-aware positional features. These features are added to token embeddings and mapped by a lightweight MLP to angular offsets that modulate the standard RoPE phases. Extensive experiments on LLaDA and DREAM demonstrate that MDLMPE generally outperforms conventional positional encoding methods across supervised fine-tuning, pretraining, zero-shot evaluation, and block-diffusion settings. Further ablations show that the complete combination of availability state, Gaussian locality, spectral basis, and embedding injection yields the strongest result. These results establish the evolving token-availability distribution as a useful positional signal for masked diffusion language models.
Tong-Tong Ling, Hang Lei, Feng Xiao et al.· 0 citations
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