ConvergeFlow: Language Flow with Provable Convergence to Token Embeddings
2026-08-24 • Computation and Language
Computation and LanguageArtificial IntelligenceMachine Learning
AI summaryⓘ
The authors introduce ConvergeFlow, a new type of language model that works with continuous embeddings instead of discrete tokens. Unlike previous models that needed extra steps to make sure outputs were valid words, ConvergeFlow restricts the model to produce only valid token embeddings by design. They prove mathematically that their approach reliably generates valid tokens and show through experiments on a text dataset that it performs as well as current models. This suggests their method could be a promising new direction for language modeling.
language modelscontinuous embeddingsflow-based modelsdiffusion modelscross entropymean squared errortoken embeddingsflow matchinggenerative perplexityOpenWebText
Authors
Na Li, Yuchen Jiao, Changxiao Cai, Gen Li
Abstract
Recent advances in continuous diffusion and flow-based language models (LMs) have achieved performance competitive with discrete LMs. However, existing continuous frameworks still rely on decoders supervised with cross entropy (CE) because the flow trajectories are not guaranteed to terminate at valid token embeddings. Motivated by this limitation, we introduce \textbf{ConvergeFlow}, an embedding-space flow-based LM, which constrains the data predictor to the convex hull of token embeddings and trains it solely with the mean squared error objective induced by flow matching. Under suitable regularity conditions, we prove that the resulting flow converges to valid token embeddings despite errors in the data predictor, enabling direct token prediction without a CE-supervised decoder. We further develop three sampling mechanisms for controlling the trade-off between the generative perplexity and entropy. Experiments on OpenWebText demonstrate that ConvergeFlow achieves performance competitive with existing continuous and discrete diffusion LMs. These findings demonstrate the potential of the flow-based paradigm for language modeling. Our code is available at https://github.com/Na-Li66/ConvergeFlow.