On the differential invariants of a family of diffusion equations

The equivalence transformation algebra $L_{\cal E}$ for the class of equations $u_t -u_{xx}=f(u, u_x) $ is obtained. After getting the differential invariants with respect to $L_{\cal E}$, some results which allow to linearize a subclass of equations are showed. Equations like the standard deterministic KPZ equation fall in this subclass.