EFF-Grasp: Energy-Field Flow Matching for Physics-Aware Dexterous Grasp Generation

Denoising generative models have recently become the dominant paradigm for dexterous grasp generation, owing to their ability to model complex grasp distributions from large-scale data. However, existing diffusion-based methods typically formulate generation as a stochastic differential equation (SDE), which often requires many sequential denoising steps and introduces trajectory instability that can lead to physically infeasible grasps. In this paper, we propose EFF-Grasp, a novel Flow-Matching-based framework for physics-aware dexterous grasp generation. Specifically, we reformulate grasp synthesis as a deterministic ordinary differential equation (ODE) process, which enables efficient and stable generation through smooth probability flows. To further enforce physical feasibility, we introduce a training-free physics-aware energy guidance strategy. Our method defines an energy-guided target distribution using adapted explicit physical energy functions that capture key grasp constraints, and estimates the corresponding guidance term via a local Monte Carlo approximation during inference. In this way, EFF-Grasp dynamically steers the generation trajectory toward physically feasible regions without requiring additional physics-based training or simulation feedback. Extensive experiments on five benchmark datasets show that EFF-Grasp achieves superior performance in grasp quality and physical feasibility, while requiring substantially fewer sampling steps than diffusion-based baselines.

Riemannian MeanFlow for One-Step Generation on Manifolds

Flow Matching enables simulation-free training of generative models on Riemannian manifolds, yet sampling typically still relies on numerically integrating a probability-flow ODE. We propose Riemannian MeanFlow (RMF), extending MeanFlow to manifold-valued generation where velocities lie in location-dependent tangent spaces. RMF defines an average-velocity field via parallel transport and derives a Riemannian MeanFlow identity that links average and instantaneous velocities for intrinsic supervision. We make this identity practical in a log-map tangent representation, avoiding trajectory simulation and heavy geometric computations. For stable optimization, we decompose the RMF objective into two terms and apply conflict-aware multi-task learning to mitigate gradient interference. RMF also supports conditional generation via classifier-free guidance. Experiments on spheres, tori, and SO(3) demonstrate competitive one-step sampling with improved quality-efficiency trade-offs and substantially reduced sampling cost.