Discrete Diffusion Language Models progressed rapidly as an alternative to autoregressive (AR) models, motivated by their parallel generation abilities. However, for tractability, discrete diffusion models sample from a factorized distribution, which is less expressive than AR. Recent Flow Language Models (FLMs) apply continuous flows to language, transporting noise to data with a deterministic ODE that avoids factorized sampling. FLMs operate on one-hot vectors whose dimension scales with the vocabulary size, making FLMs costly to train. Moreover, since all distinct one-hot embeddings are equidistant in \\(ell_2\\), adding Gaussian noise does not have a clear semantic interpretation (unlike images, where Gaussian noise progressively degrades structure). We introduce \\(mathbb{S}\\)-FLM, a latent FLM in the hypersphere. \\(mathbb{S}\\)-FLM generates sequences by rotating vectors in \\(mathbb{S}^{d-1}\\) along a velocity field learned with cross-entropy, avoiding the overhead of materializing one-hot vectors. Previous FLMs match AR in Generative Perplexity (Gen. PPL), but samples with high likelihood are not necessarily correct in verifiable domains such as math and code. \\(mathbb{S}\\)-FLM substantially improves continuous flow language models on large-vocabulary reasoning and closes the gap to masked diffusion under standard-temperature sampling (\\(T=1\\)), while a gap remains under optimized low-temperature (\\(T=0.1\\)) decoding.<\/p>\n","protected":false},"excerpt":{"rendered":"
Discrete Diffusion Language Models progressed rapidly as an alternative to autoregressive (AR) models, motivated by their parallel generation abilities. However, for tractability, discrete diffusion models sample from a factorized distribution, which is less expressive than AR. 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