Causal discovery aims to infer a Directed Acyclic Graph (DAG) from observational data to represent causal relationships among variables. Traditional combinatorial methods search DAG spaces to identify optimal structures, while recent advances in continuous optimization improve this search process. However, integrating structural constraints informed by prior knowledge into these methods remains a substantial challenge. Existing methods typically integrate prior knowledge in a hard way, demanding precise information about causal relationships and struggling with erroneous priors. Such rigidity can lead to significant inaccuracies, especially when the priors are flawed. In response to these challenges, this work introduces the Edge Constraint Adaptive (ECA) method, a novel approach that softly represents the presence of edges, allowing for a differentiable representation of prior constraint loss. This soft integration can more flexibly adjust to both accurate and erroneous priors, enhancing both robustness and adaptability. Empirical evaluations demonstrate that our approach effectively leverages prior to improve causal structure accuracy while maintaining resilience against prior errors, thus offering significant advancements in the field of causal discovery.