Trajectory as the Teacher: Few-Step Discrete Flow Matching via Energy-Navigated Distillation

Discrete flow matching generates text by iteratively transforming noise tokens into coherent language, but may require hundreds of forward passes. Distillation uses the multi-step trajectory to train a student to reproduce the process in a few steps. When the student underperforms, the usual explanation is insufficient capacity. We argue the opposite: \emph{the trajectory is the bottleneck, not the student}. Each training trajectory is built through a chain of blind stochastic jumps with no evaluation of sequence quality; a single bad decision at an early midpoint propagates through subsequent steps, yet the student must imitate the result. Trajectory-Shaped Discrete Flow Matching (TS-DFM) replaces these blind jumps with guided navigation: a lightweight energy compass evaluates candidate continuations at each midpoint, selecting the most coherent. All shaping is training-only; inference cost is unchanged. On 170M-parameter language modeling, the shaped student at 8 steps achieves 32\% lower perplexity than the $1\,024$-step teacher while being $128\times$ faster, with gains consistent across source distributions and three evaluators of increasing scale. TS-DFM achieves the best perplexity of any discrete-generation baseline we compare against, including methods trained on $6\times$ more data or using $5\times$ larger models.