Visible light positioning has the potential to yield sub-centimeter accuracy in indoor environments, yet conventional received signal strength (RSS)-based localization algorithms cannot achieve this because their performance degrades from optical multipath reflection. However, this part of the optical received signal is deterministic due to the often static and predictable nature of the optical wireless channel. In this paper, the performance of optical channel impulse response (OCIR)-based localization is studied using an artificial neural network (ANN) to map embedded features of the OCIR to the user equipment's location. Numerical results show that OCIR-based localization outperforms conventional RSS techniques by two orders of magnitude using only two photodetectors as anchor points. The ANN technique can take advantage of multipath features in a wide range of scenarios, from using only the DC value to relying on high-resolution time sampling that can result in sub-centimeter accuracy.