Pluto has a variety of surface frosts and landforms as well as a complex atmosphere(1). There is ongoing geological activity related to the massive Sputnik Planitia glacier, mostly made of nitrogen (N-2) ice mixed with solid carbon monoxide and methane(2), covering the 4-kilometre-deep, 1,000-kilometre-wide basin of Sputnik Planitia(1,3) near the anti-Charon point. The glacier has been suggested to arise from a source region connected to the deep interior, or from a sink collecting the volatiles released planetwide(1). Thin deposits of N-2 frost, however, were also detected at mid-northern latitudes and methane ice was observed to cover most of Pluto except for the darker, frost-free equatorial regions(2). Here we report numerical simulations of the evolution of N-2, methane and carbon monoxide on Pluto over thousands of years. The model predicts N-2 ice accumulation in the deepest low-latitude basin and the threefold increase in atmospheric pressure that has been observed to occur since 1988(4-6). This points to atmospheric-topographic processes as the origin of Sputnik Planitia's N-2 glacier. The same simulations also reproduce the observed quantities of volatiles in the atmosphere and show frosts of methane, and sometimes N-2, that seasonally cover the mid-and high latitudes, explaining the bright northern polar cap reported in the 1990s(7,8) and the observed ice distribution in 2015(2). The model also predicts that most of these seasonal frosts should disappear in the next decade.