Continuous Language Diffusion as a Decoder-Interface Problem

Abstract: Gaussian-corrupted sentence embeddings have no direct linguistic interpretation, yet continuous diffusion LLMs can generate fluent text from them. We study this puzzle through Embedded Language Flows (ELF) and identify a decoder-basin mechanism: denoising succeeds when trajectories reach regions where the native decoder can read stable tokens. We introduce a diagnostic protocol for denoisability, semantic recoverability, order sensitivity, decoder compatibility, and trajectory reliability. It exposes failures hidden by scalar metrics: low mean-squared error can discard linguistic content, low perplexity can reflect low-entropy collapse, and clean latent reconstruction can coexist with a narrow decoder basin. A decoder-margin bound explains why token recovery depends on margin and local decoder sensitivity, not latent error alone. Auditing public ELF checkpoints reveals an interface phase diagram: early predictions are weakly readable, mid-trajectory disagreement marks a competition region, and late predictions enter a high-margin final-token basin. Once inside, token realization is surprisingly simple on generated ELF states: frozen T5 token-embedding lookup recovers $93$--$96\%$ of native decoder decisions, and a single linear readout reaches $97.9\%$ agreement at 32k samples, leaving about a 1.1 perplexity gap in a structured residual tail. A conservative margin gate exits $17$--$27\%$ earlier in denoising steps under an explicit diagnostic monitor. Boundary checks on LangFlow, BitstreamDiffusion, and the Continuous Latent Diffusion LLM (Cola-DLM) show that the same interface questions remain meaningful when the state object and decoder change. Continuous and latent diffusion LLMs should therefore be evaluated as representation-decoder systems.