In this article, we introduce two new estimates of the normalizing constant (or marginal likelihood) for partially observed diffusion (POD) processes, with discrete observations. One estimate is biased but non-negative and the other is unbiased but not almost surely non-negative. Our method uses the multilevel particle filter of Jasra et al. (Multilevel particle lter, arXiv:1510.04977, 2015). We show that, under assumptions, for Euler discretized PODs and a given ε> 0 in order to obtain a mean square error (MSE) of O(ε2) one requires a work of O(ε- 2.5) for our new estimates versus a standard particle filter that requires a work of O(ε- 3). Our theoretical results are supported by numerical simulations.