  In this paper we present representations of the recently introduced dilute
Birman-Wenzl-Murakami algebra. These representations, labelled by the level-$l$
B$^{(1)}_n$, C$^{(1)}_n$ and D$^{(1)}_n$ affine Lie algebras, are Baxterized to
yield solutions to the Yang-Baxter equation.
  The thus obtained critical solvable models are RSOS counterparts of the,
respectively, D$^{(2)}_{n+1}$, $A^{(2)}_{2n}$ and B$^{(1)}_n$ $R$-matrices of
Bazhanov and Jimbo. For the D$^{(2)}_{n+1}$ and B$^{(1)}_n$ algebras the RSOS
models are new. An elliptic extension which solves the Yang-Baxter equation is
given for all three series of dilute RSOS models.
