Authors: Hanru Bai, Faissal Izermine, Oscar Davis, T. Konstantin Rusch
Organizations: Max Planck Institute for Intelligent Systems · ETH Zurich · ELLIS Institute Tübingen · University of Oxford · Tübingen AI Center · Liquid AI
Flow Language Models (FLMs) have emerged as a continuous-state alternative to discrete diffusion language models, yet the role of their continuous representations in reasoning remains unclear. We investigate this question by comparing the reasoning efficiency of FLMs and discrete diffusion models, measured by solution accuracy under matched denoising steps. Unlike discrete diffusion, which passes categorical states between denoising steps, FLMs evolve a continuous sequence representation throughout denoising and decodes it into discrete tokens only at the end. Our theoretical analysis shows, from a superposition perspective, how information retained in these continuous states can benefit reasoning. Intermediate-state interventions provide further empirical support for this theoretical account, showing that removing information about alternative candidates reduces subsequent solution recovery. Together, these findings show that FLMs allow evidence for multiple candidates to persist and inform subsequent reasoning before a discrete answer is produced. Furthermore, our experiments on maze planning and Sudoku tasks show that FLMs achieve greater reasoning efficiency in the few-step regime: FLMs achieves higher sequence accuracy than discrete diffusion baselines at matched model sizes and small denoising steps. On maze planning tasks, FLMs can also achieve comparable accuracy with smaller models. For example, on Maze15, FLM reaches the 95% accuracy target at 64 denoising steps with 36.5% fewer parameters than MDLM. These findings point to continuous state spaces as a promising foundation for reasoning models that require fewer refinement steps.
Flow matching enables language generation in few steps, but whether additional integration steps improve reasoning remains unclear. We prove that a flow parameterized by a two-layer Transformer can solve graph reachability, with the required number of integration steps increasing with the target's distance from the root. Yet, standard flow language models can fail to benefit from additional steps on reasoning tasks. We attribute this limitation to objectives that supervise each time point independently, without explicitly training successive steps to build on one another. To address this, we instead train through the model's own latent rollout over a randomly sampled subinterval of [0, 1], decoding only at the endpoint. On ProsQA, this raises accuracy to 97% and enables performance to improve with additional integration steps. For the longer rollouts required by reasoning tasks such as Sudoku and Maze, retracting the latent state onto a sphere stabilizes the dynamics and yields substantial gains over baselines with more than three times as many parameters. Sampling multiple rollouts further improves performance when paired with a parameter-free selection score, although reliable selection remains challenging for longer answers. Together, these results establish a theoretical basis for reasoning with flows and show how rollout training, stable latent dynamics, and rollout selection help realize this capacity in practice.
Faissal Izermine, Hanru Bai, Oscar Davis +1
Max Planck Institute for Intelligent Systems · ELLIS Institute Tübingen · ETH Zurich +3
Masked Diffusion Models (MDMs) promise fast, parallel language generation, but their reverse transition factorises across token positions -- an approximation that breaks down in the few-step sampling regime where parallel generation ought to provide the greatest efficiency gains. Flow Language Models (FLMs) sidestep this limitation by learning a continuous flow that transports noise toward clean sequences represented in Euclidean space, inducing a flow map that can be distilled for single-step generation. However, this makes complex tasks requiring multi-step reasoning problematic for FLMs, as FLMs are forced to decode every token during generation. To address this, we introduce Masked Language Flow Models (MLFMs), which incorporate masking into FLMs using a continuous stochastic interpolant to bridge partially masked and clean sequences. This design enables conditional generation via continuous flows and allows pretrained MDMs to be converted into MLFMs through a simple, lightweight adaptation. Leveraging this flexibility, we propose a novel sampler that alternates continuous denoising with the discrete unmasking of confident tokens to better support multi-step reasoning. We evaluate our approach on GSM8K and MT-Bench and find, for the first time, that flow-based language models can be scaled to solve downstream reasoning and instruction-following tasks.
Iskander Azangulov, Kianoosh Ashouritaklimi, Leo Zhang +2
Structured reasoning requires making and revising interdependent decisions to reach a globally consistent solution. Existing architectures struggle with this: autoregressive models commit sequentially and cannot revise earlier decisions, while masked diffusion models often require careful decoding schemes to coordinate interdependent predictions. We introduce Flow Reasoning Models (FRMs), a novel framework for structured reasoning that adapts continuous flows over discrete structured outputs with a simple recurrent refinement mechanism. By self-conditioning a flow model on its own past outputs, we turn one-shot denoising into iterative solution refinement. This lets FRMs make and revise decisions in parallel, efficiently coordinating interdependent choices across solutions. Yet conventional self-conditioning becomes unreliable at greater recurrent depth due to exposure bias between one-step training predictions and recursively generated inference states. We address this mismatch with Fixed-Point Forcing (FPF), which trains FRMs on states produced by their own inference dynamics while preserving the standard flow-matching objective. FRMs achieve solve rates of 99.5%, 100.0%, and 99.9% on Sudoku-Extreme, Zebra, and Maze-Unique, respectively. On Sudoku-Extreme, FRMs achieve higher peak accuracy than the evaluated masked-diffusion and specialized reasoning baselines while remaining highly compute-efficient, matching the next-best method's 98.7% peak solve rate with 44× fewer inference FLOPs.
Alec Helbling, Andrey Bryutkin, Mauro Martino +3
1Georgia Tech · 3MIT-IBM Computing Research Lab · 4IBM Research +1