Synthesizing diverse and accurate grasps with multi-fingered hands is an important yet challenging task in robotics. Previous efforts focusing on generative modeling have fallen short of precisely capturing the multi-modal, high-dimensional grasp distribution. To address this, we propose exploiting a special kind of Deep Generative Model (DGM) based on Normalizing Flows (NFs), an expressive model for learning complex probability distributions. Specifically, we first observed an encouraging improvement in diversity by directly applying a single conditional NFs (cNFs), dubbed FFHFlow-cnf, to learn a grasp distribution conditioned on the incomplete point cloud. However, we also recognized limited performance gains due to restricted expressivity in the latent space. This motivated us to develop a novel flow-based d Deep Latent Variable Model (DLVM), namely FFHFlow-lvm, which facilitates more reasonable latent features, leading to both diverse and accurate grasp synthesis for unseen objects. Unlike Variational Autoencoders (VAEs), the proposed DLVM counteracts typical pitfalls such as mode collapse and mis-specified priors by leveraging two cNFs for the prior and likelihood distributions, which are usually restricted to being isotropic Gaussian. Comprehensive experiments in simulation and real-robot scenarios demonstrate that our method generates more accurate and diverse grasps than the VAE baselines. Additionally, a run-time comparison is conducted to reveal its high potential for real-time applications.