Counterfactual explanations play a pivotal role in explainable artificial intelligence (XAI) by offering intuitive, human-understandable alternatives that elucidate ma- chine learning model decisions. Despite their significance, existing methods for generating counterfactuals often require constant access to the predictive model, involve computationally intensive optimization for each instance and lack the flex- ibility to adapt to new user-defined constraints without retraining. In this paper, we propose DiCoFlex, a novel model-agnostic, conditional generative framework that produces multiple diverse counterfactuals in a single forward pass. Leveraging conditional normalizing flows trained solely on labeled data, DiCoFlex addresses key limitations by enabling real-time user-driven customization of constraints such as sparsity and actionability at inference time. Extensive experiments on standard benchmark datasets show that DiCoFlex outperforms existing methods in terms of validity, diversity, proximity, and constraint adherence, making it a practical and scalable solution for counterfactual generation in sensitive decision-making domains.