On the design space of continuous diffusion language models

Continuous diffusion language models (CDLMs) promise to bring the benefits of continuous flow modelling to language, including accelerated sampling and controllable generation. The field has grown rapidly, and the capabilities of CDLMs have begun to rival those of discrete diffusion. Yet, unlike for continuous modalities such as images or videos, our grasp of the levers that matter when training CDLMs remains limited. In this work, we focus on two of these levers, namely self-conditioning and embedding geometry, and shed light on some of the mechanisms behind them, which in turn suggest cheaper and more effective designs. We begin by showing that self-conditioning corrects a train/inference mismatch by exposing the model to inference-like states that are otherwise rare during training. These gains can be recovered without an extra forward pass by a two-level interpolant, coined $\mathrm{DoubleCat}$, which improves TinyGSM accuracy more than threefold. Self-conditioning also aids in recognising tokens dominated by large-norm Gaussians—an issue known as token identifiability. To address it directly, we introduce discrete reveals to $\mathrm{DoubleCat}$, yielding $\mathrm{SemiCat}$, which achieves discrete diffusion-level performance on TinyGSM. At the $1.7$B scale, $\mathrm{SemiCat}$ outperforms discrete diffusion on four of six likelihood-based evaluations, and surpasses one-hot flows on unconditional generation. On embedded spaces, we find that cross-entropy drives embeddings towards a geometry whose decoding error rate closely matches the one-hot one. We briefly explore a range of further options, such as hybrid corruption processes and noise schedules, including asynchronous ones. We believe this exploration can help the community better understand and advance the design space of CDLMs.