In many applications of audio signal processing, accurate descriptions of the acoustic environment in which the signal is observed is crucial for the success of the processing task. The acoustic character of a room is often compactly represented using an impulse response or transfer function. However, this description is point-wise in the sense of corresponding to pairs of source-sensor locations. Thus, it is in practice not feasible to obtain a complete acoustic description of a room through direct measurement due to the sheer scale of the problem. To address this issue, this project proposes an interpolation, inference, and uncertainty quantification framework for the characterization of acoustic environments based on the concept of optimal mass transport. The proposal aims to construct flexible tools for computing complete acoustic descriptions using only a small set of measurements. This is achieved by incorporating physical models, as well as geometric considerations and stochastic characterizations. This also allows for determining estimation theoretically optimal ways of collecting measurements, paving the way for low-cost modes of constructing descriptions of room acoustics.