Geometric acoustics is an efficient approach to room acoustics modeling, governed by the canonical time-dependent rendering equation. Acoustic radiance transfer (ART) solves the equation through discretization, modeling the time- and direction-dependent energy exchange between surface patches given with flexible material properties. We introduce DART, a differentiable and efficient implementation of ART that enables gradient-based optimization of material properties. We evaluate DART on a simpler variant of the acoustic field learning task, which aims to predict the energy responses of novel source-receiver settings. Experimental results show that DART exhibits favorable properties, e.g., better generalization under a sparse measurement scenario, compared to existing signal processing and neural network baselines, while remaining a simple, fully interpretable system.