ModeFlow: Breaking the Connectivity Barrier of One-Step Flow Policies

One-step flow policies enable efficient action generation. However, we identify a fundamental connectivity barrier. Mapping connected Gaussian noise through a continuous generator produces a proposal distribution with connected support, so when high-value behaviors occupy separated regions, the policy necessarily places probability mass on the low-value bridges between them, and suppressing that mass below $\delta$ forces the generator's Lipschitz constant to grow as $\Omega (D/\delta )$. We formalize this barrier and derive a Gaussian-isoperimetric lower bound on the bridge mass. To overcome this challenge, we propose **ModeFlow**, a mode-conditioned one-step MeanFlow policy that discovers discrete behavior modes from offline trajectories, conditions the generator and critic on mode labels, and stratifies a fixed proposal budget across modes. This allows the policy to represent separated behaviors as distinct proposal branches while retaining efficient one-step generation. We further prove the return improvement of **ModeFlow** over one-step policies of this class, as the bridge mass induces a nonzero probability of missing the optimal behavior. Experiments demonstrate that **ModeFlow**, consistently outperforms the baselines across the Robomimic and OGBench tasks, with particularly large gains on long-horizon manipulation. On the most challenging Cube-triple-task5, \method achieves $98.4\%$ success while all baselines fail.