Deep learning models have shown incredible performance on numerous image recognition, classification, and reconstruction tasks. Although very appealing and valuable due to their predictive capabilities, one common threat remains challenging to resolve. A specifically trained attacker can introduce malicious input perturbations to fool the network, thus causing potentially harmful mispredictions. Moreover, these attacks can succeed when the adversary has full access to the target model (white-box) and even when such access is limited (black-box setting). The ensemble of models can protect against such attacks but might be brittle under shared vulnerabilities in its members (attack transferability). To that end, this work proposes a novel diversity-promoting learning approach for the deep ensembles. The idea is to promote saliency map diversity (SMD) on ensemble members to prevent the attacker from targeting all ensemble members at once by introducing an additional term in our learning objective. During training, this helps us minimize the alignment between model saliencies to reduce shared member vulnerabilities and, thus, increase ensemble robustness to adversaries. We empirically show a reduced transferability between ensemble members and improved performance compared to the state-of-the-art ensemble defense against medium and high strength white-box attacks. In addition, we demonstrate that our approach combined with existing methods outperforms state-of-the-art ensemble algorithms for defense under white-box and black-box attacks.