Abstract: Differentiable planning network architecture has shown to be powerful in solving transfer planning tasks while it possesses a simple end-to-end training feature. Much related work that has been proposed in literature is inspired by a design principle in which a recursive network architecture is applied to emulate backup operations of a value iteration algorithm. However, existing frameworks can only learn and plan effectively on domains with a lattice structure, i.e., regular graphs embedded in a particular Euclidean space. In this paper, we propose a general planning network called Graph-based Motion Planning Networks (GrMPN). GrMPN will be able to i) learn and plan on general irregular graphs, hence ii) render existing planning network architectures special cases. The proposed GrMPN framework is invariant to task graph permutation, i.e., graph isomorphism. As a result, GrMPN possesses an ability that is data-efficient and strong at generalization strength. We demonstrate the performance of two proposed GrMPN methods against other baselines on three domains ranging from 2D mazes (regular graph), path planning on irregular graphs, and motion planning (an irregular graph of robot configurations).