Geometric acoustics is an efficient framework for room acoustics modeling, governed by the canonical time-dependent rendering equation. Acoustic radiance transfer (ART) solves the equation by discretization, modeling time- and direction-dependent energy exchange between surface patches with flexible material properties. We introduce DART, an efficient, differentiable implementation of ART that enables gradient-based optimization of material properties. We evaluate DART on a simpler variant of acoustic field learning that aims to predict energy responses for novel source-receiver configurations. Experimental results demonstrate that DART generalizes better under sparse measurement scenarios than existing signal processing and neural network baselines, while maintaining simplicity and full interpretability. We open-source our implementation.