Latent Reasoning with Normalizing Flows
Guancheng Tu, Xiangjun Fu, Suhao Yu, Yao Tang, Haoqiang Kang, Lianhui Qin, Yizhe Zhang, Jiatao Gu
NF-CoT embeds a TARFlow-style normalizing flow directly inside an LLM backbone to handle reasoning steps as continuous latent states rather than discrete tokens. Text and latent positions share the same causal stream and KV cache, so the model gets exact likelihoods over compressed "thoughts" distilled from explicit chain-of-thought, plus support for policy-gradient optimization in latent space. On code-generation benchmarks it beats both explicit CoT and prior latent-reasoning methods (e.g., Coconut) while cutting intermediate token cost — though the margin details aren't in the abstract.
No production traction yet. Zero citations and the GitHub repos are purely aggregator/tracking lists with no implementation work. This is very fresh research with interesting engineering implications for inference efficiency, but nothing is shipping from it.
Large language models often improve reasoning by generating explicit chain-of-thought (CoT), demonstrating the importance of intermediate computation. However, textual CoT forces this computation through a discrete, serial, and communication-oriented token stream: each reasoning step must be verbalized before the model can proceed, even when the underlying update is semantic, uncertain, or only partially formed. Latent reasoning offers a higher-bandwidth alternative by performing intermediate computation in compact continuous states before committing to text. Yet existing latent-reasoning methods often sacrifice key advantages that make CoT effective in autoregressive language models, including native left-to-right generation, probabilistic sampling, compatibility with KV-cache decoding, and tractable likelihood estimation. We propose NF-CoT, a latent reasoning framework that preserves these advantages by modeling continuous thoughts with normalizing flows. NF-CoT instantiates a TARFlow-style normalizing flow inside the LLM backbone, defining a tractable probability model over compact continuous thoughts distilled from explicit CoT. Continuous-thought positions are generated by an NF head, while text positions are generated by the standard LM head within the same causal stream. This design provides exact likelihoods for latent thoughts, enables probabilistic left-to-right decoding with the original KV cache, and supports direct policy-gradient optimization in the latent reasoning space. On code-generation benchmarks, NF-CoT improves pass rates over explicit-CoT and prior latent-reasoning baselines while substantially reducing intermediate-reasoning cost.