Full-spectrum out-of-distribution (F-OOD) detection aims to accurately recognize in-distribution (ID) samples while encountering semantic and covariate shifts simultaneously. However, existing out-of-distribution (OOD) detectors tend to overfit the covariance information and ignore intrinsic semantic correlation, inadequate for adapting to complex domain transformations. To address this issue, we propose a Likelihood-Aware Semantic Alignment (LSA) framework to promote the image-text correspondence into semantically high-likelihood regions. LSA consists of an offline Gaussian sampling strategy which efficiently samples semantic-relevant visual embeddings from the class-conditional Gaussian distribution, and a bidirectional prompt customization mechanism that adjusts both ID-related and negative context for discriminative ID/OOD boundary. Extensive experiments demonstrate the remarkable OOD detection performance of our proposed LSA especially on the intractable Near-OOD setting, surpassing existing methods by a margin of $15.26\%$ and $18.88\%$ on two F-OOD benchmarks, respectively.