Recent generative recommenders improve scalability by retrieving items through token generation instead of traditional ranking over large candidate sets. Yet their training signals are still dominated by discrete code prediction, which overlooks the soft assignment information naturally produced by the tokenizer. This mismatch limits semantic transfer from the tokenizer to the recommender and may hurt overall optimization. We tackle this limitation by introducing a distribution-based supervision scheme for generative recommendation, where multi-level codebook probabilities are treated as soft semantic targets. On top of this design, we develop SODA, a plug-and-play alignment framework that adopts a BPR-style contrastive objective to align recommender representations with target-side distributional representations against negative ones. The proposed method enriches training with finer semantic cues while leaving the decoding stage unchanged. Experimental studies on multiple real-world benchmarks demonstrate that SODA consistently strengthens diverse generative recommendation architectures. Code is available at https://github.com/freyasa/SODA

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