Colour realism plays an important role in computer graphics and visualization. In this paper, we present a new approach to direct volume rendering based on the Kubelka-Munk theory of diffuse reflectance. We show that not only the Kubelka-Munk theory facilitates a correct spectral volume rendering integral suitable for both solid objects and amorphous matters in volume datasets, but also provides volume visualization with more accurate optical effects than the traditional volume rendering integral based on the RGB accumulation. We discuss the design of transfer functions for specifying absorption and scattering coefficients, and the use of post-illumination for integrating pre-processed reflectance images in real time. We demonstrate the optical realism achieved by this approach with a combination of several natural and artificial colour datasets. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Image Generation: Display Algorithms I.3.7 [Computer G...