Density Matrix Exponentiation is a technique for simulating Hamiltonian dynamics when the Hamiltonian to be simulated is available as a quantum state. In this paper, we present a natural analogue to this technique, for simulating Markovian dynamics governed by the well known Lindblad master equation. For this purpose, we first propose an input model in which a Lindblad operator is encoded into a quantum state . Then, given access to copies of the state , the task is to simulate the corresponding Markovian dynamics for time . We propose a quantum algorithm for this task, called Wave Matrix Lindbladization, and we also investigate its sample complexity. We show that our algorithm uses samples of to achieve the target dynamics, with an approximation error of .