Reasoning with Continuous Latent Diffusion

Continuous diffusion generates complete reasoning solutions through iterative refinement in latent space. We introduce Latent Flow Reasoning Models (LFRMs), an ELF-based training and inference recipe. Our experiments show that accurate decoding alone does not ensure effective generation, motivating compact representations learned from multiple layers of a strong autoregressive teacher. Their decomposition also enables asynchronous denoising at different rates. We show that prompt encodings need only preserve the information required for the correct text-conditional score, rather than exactly match teacher features, and use a staged curriculum to learn a compact prompt encoder that replaces the teacher Transformer at inference. We adapt DiffusionNFT to learned self-conditioning guidance and incorporate gold-solution endpoints to supplement sparse rewards. With 90M and 638M denoising backbones, our strongest supervised results outperform reported continuous-diffusion baselines at comparable backbone scales on mathematical reasoning and code generation. NFT further improves single-sample accuracy on math and code, and majority-vote performance on mathematics. Code will be available at: https://anonymous.4open.science/r/LFRM-98B5/.