Generalized Category Discovery (GCD) aims to identify both known and novel categories from partially labeled data, reflecting more realistic open-world learning scenarios. However, most existing methods rely solely on one-hot discriminative supervision, leading to overfitting on seen classes and poor generalization to unseen ones. Recent advances introduce large language models (LLMs) to incorporate external semantics, yet they often suffer from semantic–label misalignment and weak semantic integration during training. We propose GenDis, a Generative–Discriminative Dual-View Co-Training framework that unifies discriminative classification and semantic label generation within an LLM. Discriminative pseudo-labels guide the formation of a separable generative latent space, enabling semantically meaningful supervision for novel classes. To ensure consistency between the two views, we employ Canonical Correlation Analysis (CCA)-based alignment and a curriculum-guided, dispersion-aware pseudo-labeling strategy for iterative refinement. Extensive experiments on five GCD benchmarks demonstrate that GenDis substantially outperforms prior methods, validating the effectiveness of dual-view co-training with semantically enriched supervision. The anonymized repository is available at https://anonymous.4open.science/r/GenDis.