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 La Niñas and extreme Eastern Pacific 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 effectively simulates key aspects of 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. By examining NG-LIM simulations, we find that, as observed, El Niños exhibit stronger anomalies and evolve more rapidly than La Niñas. The improved NG-LIM also generates a broad library of synthetic events, which can supplement the limited observational record.