In a molecular communication system, molecules convey the information by traversing from the transmitter to the receiver through the medium.  The molecular communication channel is modeled as an additive inverse Gaussian noise channel, the input of which is the release times of the molecules. This talk is on the capacity-achieving input distribution for such a channel, where the release time is subject to both peak and average constraints. Several properties of the capacity-achieving input are established. A numerical method for computing the optimal input distribution is developed. The result complements some existing bounds on the capacity.