ESP: Energy-Score Policy for One-Step Multimodal Action Generation

Flow-based vision-language-action (VLA) policies offer strong expressivity for action generation, but suffer from a fundamental inefficiency: multi-step inference is required to recover action structure from uninformative Gaussian noise, leading to a poor efficiency-quality trade-off under real-time constraints. We address this issue by rethinking the role of the starting point in generative action modeling. Instead of shortening the sampling trajectory, we propose CF-VLA, a coarse-to-fine two-stage formulation that restructures action generation into a coarse initialization step that constructs an action-aware starting point, followed by a single-step local refinement that corrects residual errors. Concretely, the coarse stage learns a conditional posterior over endpoint velocity to transform Gaussian noise into a structured initialization, while the fine stage performs a fixed-time refinement from this initialization. To stabilize training, we introduce a stepwise strategy that first learns a controlled coarse predictor and then performs joint optimization. Experiments on CALVIN and LIBERO show that our method establishes a strong efficiency-performance frontier under low-NFE (Number of Function Evaluations) regimes: it consistently outperforms existing NFE=2 methods, matches or surpasses the NFE=10 $π_{0.5}$ baseline on several metrics, reduces action sampling latency by 75.4%, and achieves the best average real-robot success rate of 83.0%, outperforming MIP by 19.5 points and $π_{0.5}$ by 4.0 points. These results suggest that structured, coarse-to-fine generation enables both strong performance and efficient inference. Our code is available at https://github.com/EmbodiedAI-RoboTron/CF-VLA.

Vision-language-action (VLA) policies leverage pretrained vision-language backbones to achieve strong cross-task generalization. A leading design couples this backbone with a dedicated continuous action head trained via diffusion or flow matching. However, such heads rely on iterative multi-step sampling, for example 10 Euler steps in $\pi_{0.5}$. This creates an inference bottleneck that produces stop-and-go movement in the robot and slower task completion. We introduce IMLE-VLA, which replaces the iterative action head with a single-step conditional generator trained via conditional Implicit Maximum Likelihood Estimation (cIMLE). The cIMLE objective promotes multimodal action coverage, avoiding the mode collapse of naive regression heads while eliminating multi-step sampling entirely. When IMLE-VLA is applied to $\pi_{0.5}$, it increases inference frequency 3.67x (55 Hz vs. 15 Hz), enabling up to 11x higher action throughput. On the 40-task LIBERO benchmark, IMLE-VLA achieves the highest average success rate (98.0%) among all baselines while leading in inference frequency. Under the test-time perturbations of LIBERO-plus, IMLE-VLA retains $\pi_{0.5}$'s robustness while other baselines degrade sharply, confirming that the cIMLE head preserves generalization. Real-world experiments on a Franka Emika Panda across four tasks demonstrate smoother motion (2.2x to 3.0x lower jerk) and faster task completion, with IMLE-VLA outperforming $\pi_{0.5}$ on every task and reducing average VLA inference time per episode by 3.9x to 6.6x. Videos and code are available at https://kianhk6.github.io/IMLE-VLA/

Generative models such as diffusion and flow matching have become dominant paradigms for visuomotor policy learning, yet their reliance on iterative denoising incurs high inference latency incompatible with real-time robotic control. We present Fast Legendre-polynomial Action policy via Sparse History-anchored flow (FLASH Policy), which replaces discrete action-chunk generation with continuous Legendre polynomial trajectory representation. Specifically, by fitting expert demonstrations under sparse temporal sampling, FLASH enables a single inference to cover a significantly extended action horizon. To further accelerate generation, FLASH initiates the flow matching process from history polynomial coefficients rather than uninformative Gaussian noise, shortening the transport distance and enabling accurate single-step inference. Moreover, analytic polynomial differentiation directly provides desired velocity feed-forward signals to the torque controller without numerical approximation. Extensive experiments on five simulated and two real-world manipulation tasks demonstrate that FLASH achieves state-of-the-art success rates ($\ge 92\%$ across all tasks), a per-episode inference time of $31.40\,ms$ (up to $175\times$ faster than diffusion policies and $18\times$ faster than prior flow matching policies), up to $4\times$ faster training convergence than ACT, and $5\times$ to $7\times$ reduction in controller tracking error compared to discrete-action baselines.