Synthesizing diverse dexterous grasps from uncertain partial observation is an important yet challenging task for physically intelligent embodiments. Previous works on generative grasp synthesis fell short of precisely capturing the complex grasp distribution and reasoning about shape uncertainty in the unstructured and often partially perceived reality. In this work, we introduce a novel model that can generate diverse grasps for a multi-fingered hand while introspectively handling perceptual uncertainty and recognizing unknown object geometry to avoid performance degradation. Specifically, we devise a Deep Latent Variable Model (DLVM) based on Normalizing Flows (NFs), facilitating hierarchical and expressive latent representation for modeling versatile grasps. Our model design counteracts typical pitfalls of its popular alternative in generative grasping, i.e., conditional Variational Autoencoders (cVAEs) whose performance is limited by mode collapse and miss-specified prior issues. Moreover, the resultant feature hierarchy and the exact flow likelihood computation endow our model with shape-aware introspective capabilities, enabling it to quantify the shape uncertainty of partial point clouds and detect objects of novel geometry. We further achieve performance gain by fusing this information with a discriminative grasp evaluator, facilitating a novel hybrid way for grasp evaluation. Comprehensive simulated and real-world experiments show that the proposed idea gains superior performance and higher run-time efficiency against strong baselines, including diffusion models. We also demonstrate substantial benefits of greater diversity for grasping objects in clutter and a confined workspace in the real world.