Due to the inherent uncertainty in their deformability during motion, previous methods in rope manipulation often require hundreds of real-world demonstrations to train a manipulation policy for each rope, even for simple tasks such as rope goal reaching, which hinder their applications in our ever-changing world. To address this issue, we introduce GenORM, a framework that allows the manipulation policy to handle different deformable ropes with a single real-world demonstration. To achieve this, we augment the policy by conditioning it on deformable rope parameters and training it with a diverse range of simulated deformable ropes so that the policy can adjust actions based on different rope parameters. At the time of inference, given a new rope, GenORM estimates the deformable rope parameters by minimizing the disparity between the grid density of point clouds of real-world demonstrations and simulations. With the help of a differentiable physics simulator, we require only a single real-world demonstration. Empirical validations on both simulated and real-world rope manipulation setups clearly show that our method can manipulate different ropes with a single demonstration and significantly outperforms the baseline in both environments (62% improvement in in-domain ropes, and 15% improvement in out-of-distribution ropes in simulation, 26% improvement in real-world), demonstrating the effectiveness of our approach in one-shot rope manipulation.