Learning from demonstrations (LfD) typically relies on large amounts of action-labeled expert trajectories, which fundamentally constrains the scale of available training data. A promising alternative is to learn directly from unlabeled video demonstrations. However, we find that existing methods tend to encode latent actions that share little mutual information with the true robot actions, leading to suboptimal control performance. To address this limitation, we introduce a novel framework that explicitly maximizes the mutual information between latent actions and true actions, even in the absence of action labels. Our method leverage the variational information-bottleneck to extract action-relevant representations while discarding task-irrelevant information. We provide a theoretical analysis showing that our objective indeed maximizes the mutual information between latent and true actions. Finally, we validate our approach through extensive experiments: first in simulated robotic environments and then on real-world robotic platforms, the experimental results demonstrate that our method significantly enhances mutual information and consistently improves policy performance.