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In high dimensional robotic system, the manifold of the valid configuration space often has a complex shape, especially under constraints such as end-effector orientation or static stability. We propose a generative adversarial network approach to learn the distribution of valid robot configurations under such constraints. It can generate configurations that are close to the constraint manifold. We present two applications of this method. First, by learning the conditional distribution with respect to the desired end-effector position, we can do fast inverse kinematics even for very high degrees of freedom (DoF) systems. Then, we use it to generate samples in sampling-based constrained motion planning algorithms to reduce the necessary projection steps, speeding up the computation. We validate the approach in simulation using the 7-DoF Panda manipulator and the 28-DoF humanoid robot Talos.