We introduce $\textbf{F}$uture $\textbf{LA}$tent $\textbf{RE}$presentation Alignment ($\textbf{FLARE}$), a novel framework that integrates predictive latent world modeling into robot policy learning. By aligning features from a diffusion transformer with latent embeddings of future observations, $\textbf{FLARE}$ enables a diffusion transformer policy to anticipate latent representations of future observations, allowing it to reason about long-term consequences while generating actions. Remarkably lightweight, $\textbf{FLARE}$ requires only minimal architectural modifications -- adding a few tokens to standard vision-language-action (VLA) models -- yet delivers substantial performance gains. Across two challenging multitask simulation imitation learning benchmarks spanning single-arm and humanoid tabletop manipulation, $\textbf{FLARE}$ achieves state-of-the-art performance, outperforming prior policy learning baselines by up to 26%. Moreover, $\textbf{FLARE}$ unlocks the ability to co-train with human egocentric video demonstrations without action labels, significantly boosting policy generalization to a novel object with unseen geometry with as few as a single robot demonstration. Our results establish $\textbf{FLARE}$ as a general and scalable approach for combining implicit world modeling with high-frequency robotic control.