Large Language Continuous Diffusion Models

Despite success of discrete diffusion language models (dLMs) for fast parallel decoding, their non-smooth, high-dimensional space hinders trajectory steering for reasoning and inference acceleration. To overcome this, we present Sigma, the first large-scale (3B/8B) continuous dLM built on steerable, low-dimensional ODE/SDE latent trajectories. Trained blockwise via likelihood optimization, Sigma jointly denoises Gaussian-corrupted tokens while learning an optimal embedding geometry. To scale training, Sigma leverages pre-trained weights from existing autoregressive (AR) models for warm-starting. During inference, we identify classifier-free guidance and score temperature as essential for high-fidelity reasoning and coding. Across comprehensive math reasoning and coding evaluations against state-of-the-art discrete counterparts (masked dLMs and AR baselines), Sigma achieves competitive performance with discrete models on standard benchmarks (e.g., GSM8K, Minerva, HumanEval, MBPP) after pre-training and on challenging reasoning tasks (e.g., MATH-500, AIME) after supervised fine-tuning. Beyond performance parity, we uncover key structural properties unique to continuous dLMs: (i) embedding-space steering effectively governs the quality-diversity trade-off, yielding strong pass@k performance and (ii) continuous trajectories enable graceful degradation for low NFEs and efficient distillation. These establish continuous dLMs as a promising paradigm for efficient language generation.