Efficient optical energy transfer is key to many technologies, ranging from biosensing to photovoltaics. Here, for the first time we show that by introducing a random medium with appropriate filling factor, absorption in a specific volume can be maximized. Using both numerical simulations and an analytical diffusion model, we identify design rules to maximize absorption in the system with different geometrical and scattering properties. By combining a random medium with an open photonic cavity, we numerically demonstrate a 23-fold enhancement of the absorbed energy. We also show how absorption as high as 99% can be reached in a device as thin as 500 μm for normal incidence illumination. Finally, our data indicate that introducing a non-absorbing random medium into a light trapping system for thin solar cells can enhance absorption of energy by a factor of 2.2. This absorption enhancement, caused by the random medium, is broadband and wide-angle and can help design efficient solar cells, light trapping devices, biosensors and random lasers.