Let $M$ and $N$ be smooth manifolds of the same dimension, let $F: M \to N$ be a diffeomorphism, and let $u \in \mathcal{D}'(N)$ be a distribution. Let $F^*u \in \mathcal{D}'(M)$ denote the distributional pullback of $u$ by the diffeomorphism $F$. For each $x \in M$, let $dF_x: T_xM \to T_{F(x)}N$ be the differential of $F$ at $x$, and let $dF_x^\top: T_{F(x)}^*N \to T_x^*M$ be the cotangent pullback map defined by $dF_x^\top\eta = \eta \circ dF_x$ for every $\eta \in T_{F(x)}^*N$. Let $\dot T^*M = T^*M \setminus \{0\}$ and $\dot T^*N = T^*N \setminus \{0\}$ denote the punctured cotangent bundles. Then

\begin{align*} \operatorname{WF}(F^*u)=\{(x,dF_x^\top\eta)\in \dot T^*M:(F(x),\eta)\in \operatorname{WF}(u)\}. \end{align*}