Recently, Heller et al. reported length-dependent effects on the relative photoluminescence (PL) quantum yield of single walled carbon nanotubes (SWNTs) [Heller et al J. Am. Chem. Soc. 2004, 126, 14567-14573]. We propose a simple model involving thermal diffusion of excitons along the nanotube axis and quenching at the ends, to explain the observed trend in their data. By fitting to our model, we extract a diffusion coefficient of 6 cm(2)/s for excitons in SWNTs. Assuming a mono exponential decay of exciton PL, we also predict that effective length-dependent PL lifetimes for these excitons lie in the range of 1 - 27 ps. Experimental observations are shown to be consistent with stochastic rather than wavepacket-like exciton migration, which is in agreement with ultrafast excitonic dephasing. Edge effects seem to limit the use of short SWNTs in imaging and optical sensing applications.