In this talk we explore the fluctuations around the porous medium equation, examining their connections to large deviations principles and gradient flow structures. We first show that a suitably rescaled zero range process converges to the porous medium equation in its hydrodynamic limit. We then prove a full large deviations principle in this setting. In a third part, we link this to a formal gradient flow interpretation of the porous medium equation by deducing a De Giorgi entropy dissipation principle from the large deviations and reversibility.