  We show how to build a multi-scale entanglement renormalization ansatz (MERA)
representation of the ground state of a many-body Hamiltonian $H$ by applying
the recently proposed \textit{tensor network renormalization} (TNR) [G. Evenbly
and G. Vidal, arXiv:1412.0732] to the Euclidean time evolution operator
$e^{-\beta H}$ for infinite $\beta$. This approach bypasses the costly energy
minimization of previous MERA algorithms and, when applied to finite inverse
temperature $\beta$, produces a MERA representation of a thermal Gibbs state.
Our construction endows TNR with a renormalization group flow in the space of
wave-functions and Hamiltonians (and not just in the more abstract space of
tensors) and extends the MERA formalism to classical statistical systems.
