LangFlow: Continuous Diffusion Rivals Discrete in Language Modeling

Continuous diffusion has served as a foundation for high-fidelity, controllable, and few-step generation across continuous data modalities such as images, videos, and molecular structures. However, in language modeling, prior continuous diffusion language models (DLMs) lag behind discrete counterparts. Existing categorical and simplex-based approaches operate over extremely large and sparse language spaces, while prior embedding-space approaches avoid this sparsity but lack a well-selected design space. In this work, we close this gap with LangFlow by connecting embedding-space DLMs to Flow Matching, alongside three key innovations: (1) we derive a novel ODE-based NLL bound for principled evaluation of continuous flow-based language models; (2) we propose an information-uniform principle for setting the noise schedule, which motivates a learnable noise scheduler based on a Gumbel distribution; and (3) we revise prior training protocols by incorporating self-conditioning, which improves both likelihood and sample quality for embedding-space DLMs and behaves differently from its use in discrete diffusion. Putting everything together, LangFlow is competitive with top discrete DLMs on both perplexity (PPL) and generative perplexity (Gen. PPL), reaching a PPL of 30.0 on LM1B and 24.6 on OpenWebText. It also exceeds autoregressive baselines in zero-shot transfer on 4 out of 7 benchmarks. As the first continuous DLM shown to rival discrete diffusion in both generative quality and perplexity, LangFlow provides clear evidence that continuous diffusion is a promising paradigm for language modeling. Code will be released upon acceptance.