Reliable obstacle avoidance, which is essential for safe autonomous robot interaction with the real world, raises various challenges such as difficulties with obstacle perception and latent factor cognition impacting multi-modal obstacle avoidance. In this paper, we propose a Depth visUal Ego-motion Learning (DUEL) model, consisting of a cognitive generation network, a policy decision network and a potential partition network, to learn autonomous obstacle avoidance from expert policies. The DUEL model takes advantage of binocular vision to perceive scene depth. This serves as the input to the cognitive generation network which generates obstacle avoidance policies by maximizing its causal entropy. The policy decision network then optimizes the generation of the policies referring to expert policies. The generated obstacle avoidance policies are simultaneously transferred to the potential partition network to capture the latent factors contained within expert policies and perform multi-modal obstacle avoidance. These three core networks iteratively optimize the multi-modal policies relying on causal entropy and mutual information theorems, which are proven theoretically. Experimental comparisons with state-of-the-art models on 7 metrics demonstrate the effectiveness of the DUEL model. It achieves the best performance with an average ADE (Average Displacement Error) of 0.29 and average FDE (Final Displacement Error) of 0.55 across five different scenarios. Results show that the DUEL model can maintain an average obstacle avoidance success rate of 97% for both simulated and real world scenarios with multiple obstacles, demonstrating its success at capturing latent factors from expert policies. Our source codes are available at https://github.com/ACoTAI/DUEL .