Prompt tuning adapts vision--language models with few trainable parameters, but computing their gradients still requires backpropagation through frozen encoders. We introduce ZOMP, a forward-only method for deep multimodal prompt tuning under a limited loss-query budget. ZOMP combines shared prompt factors with a budget-indexed rank schedule and gradient-correction momentum. Early updates search a rank-one subspace; later updates activate additional components without discarding the existing optimizer state. With 5,000 training-loss queries, ZOMP achieves 68.2\% average 16-shot accuracy across 13 datasets, improving on ZIP by 6.0 points, alongside gains in base-to-new and distribution-shift generalization. On five image--text retrieval datasets, it outperforms four derivative-free baselines at both training sizes, improving average bidirectional Recall@1 over BPT-VLM by 2.63 points. An exploratory five-benchmark language diagnostic comparison examines caption discrimination beyond the retrieval galleries. Component, modality, depth, and budget studies characterize the method's benefits. ZOMP requires an internal-prompt inference interface and reduces allocated training memory relative to a matched-architecture first-order reference.

翻译：暂无翻译