We model solar irradiance variations over a broad range of timescales. 3D MHD simulations with MURAM are used to simulate Total Solar Irradiance changes on timescales of minutes to days due to convection. Changes due to surface magnetism are modelled with SATIRE-S relying on the high-cadence solar imagery from the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory. A comparison to observations shows that such a combination of SATIRE and MURAM is remarkably successful in reproducing available records of Total Solar Irradiance on timescales of minutes to decades. This demonstrates that solar magnetism and convection can account for TSI variability at all timescale it has ever been measured (with the exception of 5-minute oscillations from p-modes). We also present a comparison of our model to empirical models of solar irradiance variations.