In the last few decades, we have seen great progress in robot motion planning and control problems in which the robot has to reason about geometry, kinematics, and physics to generate a desired low-level motion. Building on this advancement, we consider task and motion planning problems in which the robot has to reason from a high-level objective, such as cooking a meal, down to such low-level details. This requires reasoning over a long horizon with hybrid decision variables. However, existing planners do not learn from the past experience of solving previous problem instances, and solve such complex planning problems from scratch every time. On the other hand, a complete learning approach would require too much experience to learn a completely detailed policy. Based on these observations, we propose to use learning to guide the search of a planner by predicting constraints that restricts the search space of the planner. We study two important challenges for predicting constraints: learning to represent complex planning scenes involving varying numbers of objects with varying size and symbolic state, and how to use a dataset of search experience for learning. We first offer a solution by focusing on the geometric aspects of task and motion planning problems that suggests promising actions based on generative adversarial networks. Then, we offer a solution for generic task and motion planning problems by proposing a representation based on the scores of previous solution attempts. We show that our algorithms can speed up planning by orders of magnitudes in challenging simulated robot domains.