Short-video misinformation detection has attracted wide attention in the multi-modal domain, aiming to accurately identify the misinformation in the video format accompanied by the corresponding audio. Despite significant advancements, current models in this field, trained on particular domains (source domains), often exhibit unsatisfactory performance on unseen domains (target domains) due to domain gaps. To effectively realize such domain generalization on the short-video misinformation detection task, we propose deep insights into the characteristics of different domains: (1) The detection on various domains may mainly rely on different modalities (i.e., mainly focusing on videos or audios). To enhance domain generalization, it is crucial to achieve optimal model performance on all modalities simultaneously. (2) For some domains focusing on cross-modal joint fraud, a comprehensive analysis relying on cross-modal fusion is necessary. However, domain biases located in each modality (especially in each frame of videos) will be accumulated in this fusion process, which may seriously damage the final identification of misinformation. To address these issues, we propose a new DOmain generalization model via ConsisTency and invariance learning for shORt-video misinformation detection (named DOCTOR), which contains two characteristic modules: (1) We involve the cross-modal feature interpolation to map multiple modalities into a shared space and the interpolation distillation to synchronize multi-modal learning; (2) We design the diffusion model to add noise to retain core features of multi modal and enhance domain invariant features through cross-modal guided denoising. Extensive experiments demonstrate the effectiveness of our proposed DOCTOR model. Our code is public available at https://github.com/ghh1125/DOCTOR.