Non-autoregressive language models are emerging as effective alternatives to autoregressive models in the field of natural language processing, facilitating simultaneous token generation. This study introduces a novel flow matching approach that employs Kullback-Leibler (KL) divergence geodesics to interpolate between initial and target distributions for discrete sequences. We formulate a loss function designed to maximize the conditional likelihood of discrete tokens and demonstrate that its maximizer corresponds to the flow matching velocity during logit interpolation. Although preliminary experiments conducted on the TinyStories dataset yielded suboptimal results, we propose an empirical sampling scheme based on a pretrained denoiser that significantly enhances performance. Additionally, we present a more general hybrid approach that achieves strong performance on more complex datasets, such as Fine Web and Lamini Instruction.

The paper presents the exact formula for the vector field that minimizes the loss for the standard flow. This formula depends analytically on a given distribution \rho_0 and an unknown one \rho_1. Based on the presented formula, a new loss and algorithm for training a vector field model in the style of Conditional Flow Matching are provided. Our loss, in comparison to the standard Conditional Flow Matching approach, exhibits smaller variance when evaluated through Monte Carlo sampling methods. Numerical experiments on synthetic models and models on tabular data of large dimensions demonstrate better learning results with the use of the presented algorithm.