Invasive Species Prevention and Forest Restoration Act This bill sets forth provisions to control invasive species and support native trees. Specifically, the bill directs the Department of Agriculture (USDA) to award grants to federal agencies, nonprofit organizations, and certain institutions for research to promote the restoration of tree species affected by non-native plant pests and noxious weeds. USDA may also award grants to implement the research or other solutions to restore forest tree species native to the United States that have suffered severe levels of mortality caused by nonnative plant pests or noxious weeds. Grants may be awarded to cooperating forestry schools, land-grant colleges or universities, state agricultural experimental stations, or nonprofit organizations. The bill also expands the authority of USDA to transfer funds to respond to an emergency in which a plant pest or noxious weed directly or indirectly threatens any segment of U.S. agricultural production. Further, USDA must enter into an agreement with the National Academy of Sciences or another nongovernmental entity to analyze available resources that federal agencies have to research, and find solutions to, nonnative plant pests and pathogens.