Precipitation estimation in mountainous regions is heavily reliant on remote sensing observations and analysis. We demonstrate that the most advanced global precipitation products underestimate extreme rainfall in mountainous regions. A study comprising over 10 000 flood-producing extreme rainfall events worldwide over the past 52 years (1973–2024) shows median underestimations of 100 mm and 225 mm for the top 5 % and 1 % extreme rainfall events, respectively. The spatial variability of rainfall is also significantly underestimated by a factor of 3 in the world’s mountains. These findings confirm the limited ability to monitor and quantify extreme rainfall in complex terrain. This work provides a novel path to systematically enhance precipitation estimates globally using a general hybrid physics–AI framework, even for the top 1 % of extreme events.