A system often exhibits more fine-grained causal relationships between a variable and its parents, which we call local independence relationships including Context-Specific Independence (CSI). It plays a crucial role in probabilistic inference and causal effect identification. However, for the continuous variables, directly searching for the local independence is infeasible and it is still unclear how to effectively discover them. To this end, we propose a novel framework to discover the local independences of continuous variables by partitioning the joint outcome space of the parent variables and imposing each partition to induce the local independence via modeling of a conditional distribution. In experiments with both static and sequential settings, we empirically demonstrated that the proposed method successfully discovers the ground truth local independencies.