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We propose a novel approach to multi-fingered grasp planning leveraging learned deep neural network models. We train a convolutional neural network to predict grasp success as a function of both visual information of an object and grasp configuration. We can then formulate grasp planning as inferring the grasp configu- ration which maximizes the probability of grasp success. We efficiently perform this inference using a gradient-ascent optimization inside the neural network using the backpropagation algorithm. Our work is the first to directly plan high quality multi- fingered grasps in configuration space using a deep neural network without the need of an external planner. We validate our inference method performing both multi- finger and two-finger grasps on real robots. Our experimental results show that our planning method outperforms existing planning methods for neural networks; while offering several other benefits including being data-efficient in learning and fast enough to be deployed in real robotic applications.