Deep learning-based medical segmentation methods suffer from the limited amount of data due to data privacy and ethical issues, which results in generalization degradation and hinders their applications in clinical scenarios. In this paper, we propose a novel data augmentation method named Adversarial Multi-Sample Interpolation (AMSI) based on adaptive interpolations among multiple latent codes to produce new data samples. AMSI first introduces an AutoDecoder to construct the latent codes for given data points and then augment the latent space through learning-based adaptive interpolations. Specifically, we design a multi-dimension interpolation among multiple samples with learnable coefficients to adaptively generate more diverse hard examples via adversarial training. Furthermore, our method generates both synthesized images and pseudo labels simultaneously, which is different against previous style-augmented methods. Additionally, the adjacent relationship between latent points will be considered for the sake of realistic appearance and smooth pseudo labels. The effectiveness and generalization ability of AMSI are validated by extensive experiments both on two segmentation tasks employing four publicly available datasets.