Abstract Linear Inverse Models (LIMs) are widely used data‐driven tools for studying El Niño Southern Oscillation (ENSO). However, standard LIMs struggle to simulate the observed asymmetry and diversity of ENSO events. Observations reveal that strong Central Pacific (CP) La Niñas and extreme Eastern Pacific (EP) El Niños occur more frequently than their counterparts, a feature standard LIMs fail to capture. We introduce a modified model, the Non‐Gaussian LIM (NG‐LIM), which transforms the LIM variables to better simulate ENSO asymmetry and diversity. Specifically, the NG‐LIM reproduces the spatial pattern of sea surface temperature (SST) skewness and the inverted U‐shaped relationship between the first two principal components of Tropical Pacific SST anomalies, reflecting more frequent strong CP La Niñas and extreme EP El Niños. NG‐LIM simulations also show El Niños that are stronger and evolve more rapidly than La Niñas. This improved inverse model generates synthetic events to supplement the limited observational record.