Offline Reinforcement Learning (RL) aims to learn policies from pre-collected datasets that capture only a subset of the environment's dynamics. The predominant approach has been to solve a constrained optimization formulation, which ensures that the policy visits state-action pairs within the support of the offline dataset. However, this approach has limited the ability to make decisions when the agent faces unknown parts of the environment at deployment time. To address the challenge of decision-making in out-of-support regions, model-based Bayes-adaptive approaches have been proposed by considering all dynamics models that could potentially be the true environment. Since it is generally infeasible to compute the posterior of all dynamics models based on the offline dataset, these approaches usually approximate the posterior by using a finite ensemble of highly probable dynamics models. Hence, the diversity of these models is the key to obtaining good policies. In this work, we propose MoDAP (Model-based Diverse Adaptive Policy Learning), an algorithm to enable the adaptive policy to make informed decisions in previously unexplored states. MoDAP adopts an iterative strategy that simultaneously training the policy and dynamics models. The policy optimization seeks to maximize expected returns across dynamics models, while the dynamics models are trained to promote policy diversification through the proposed information-theoretic objective. We evaluate MoDAP through experiments on the D4RL and NeoRL benchmarks, showcasing its performance superiority over state-of-the-art algorithms.