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Synthesizing diverse and uncertainty-aware multi-finger hand grips from partial observations remains a critical challenge in robot learning. Existing generative models struggle to model the complex grip distribution of dexterous hands and often generate unreliable or overly conservative grips, failing to account for the shape uncertainty inherent in partial point clouds. In this paper, we propose FFHFlow, a flow-based variational framework that generates diverse and robust multi-finger grips while explicitly quantifying perceptual uncertainty from partial point clouds. The proposed method overcomes the mode collapse and fixed prior constraints of conditional variational autoencoders (cVAEs) by leveraging a regularized flow-based deep latent variable model to learn a hierarchical grip manifold. Leveraging the reversibility of flow and the precise likelihood, FFHFlow internally probes shape uncertainty from partial observations and identifies novel object structures, enabling hazard-aware grip synthesis. To further enhance reliability, we integrate the flow likelihood with a discriminative grip estimator to develop an uncertainty-aware ranking strategy that prioritizes grips robust to shape ambiguity. Extensive experiments in simulations and real-world environments demonstrate that FFHFlow outperforms state-of-the-art benchmarks (including diffusion models) in terms of grip diversity and success rate, while achieving runtime-efficient sampling. Furthermore, we demonstrate its practical value in complex, constrained environments, where diversity-based sampling mitigates collisions and delivers superior performance (project page: https://sites.google.com/view/ffhflow/home/ ).
