We introduce DexDiffuser, a novel dexterous grasping method that generates, evaluates, and refines grasps on partial object point clouds. DexDiffuser includes the conditional diffusion-based grasp sampler DexSampler and the dexterous grasp evaluator DexEvaluator. DexSampler generates high-quality grasps conditioned on object point clouds by iterative denoising of randomly sampled grasps. We also introduce two grasp refinement strategies: Evaluator-Guided Diffusion and Evaluator-based Sampling Refinement. The experiment results demonstrate that DexDiffuser consistently outperforms the state-of-the-art multi-finger grasp generation method FFHNet with an, on average, 9.12% and 19.44% higher grasp success rate in simulation and real robot experiments, respectively.