Microservice systems are inherently complex and prone to failures, which can significantly impact user experience. Existing diagnostic approaches based on single-modal data such as logs, metrics, or traces cannot comprehensively capture failure patterns. For those multimodal data-based failure diagnosis methods, the dominant modality can overshadow others, hindering low-yield modalities from fully leveraging their characteristics. This paper proposes Medicine, a modal-independent microservice failure diagnosis framework based on multimodal adaptive optimization. It encodes different modalities separately to retain their unique features and employs adaptive optimization to adjust the learning pace between modalities, thereby enhancing overall diagnostic performance. Experimental results demonstrate that Medicine outperforms existing single-modal and multimodal diagnostic approaches on two public datasets, with F1-score improving by 15.72% to 35.54%. Even in cases where individual modal data is missing or of lower quality, Medicine maintains high diagnostic accuracy.