2. Let the volume of tetrahedron $ABCD$ be $V$, $E$ be the midpoint of edge $AD$, and point $F$ be on the extension of $AB$ such that $BF = AB$. The plane through points $C$, $E$, and $F$ intersects $BD$ at point $G$. Then the volume of tetrahedron $CDGE$ is
2. $\frac{1}{3} V$.

As shown in Figure 3, it is easy to see that
$V_{\text {WWibuncis }}$
$=V_{\text {m flower position }}$.
By Menelaus' Theorem, we know
$$
\frac{B G}{G D} \cdot \frac{D E}{E A} \cdot \frac{A F}{F B}=1 .
$$

Therefore, $\frac{B G}{G D}=\frac{1}{2}$.
Then, $S_{\text {. } \triangle A R C}=\frac{1}{2} D E \cdot D G \sin \angle A D B=\frac{1}{3} S_{\text {Um }}$. Thus, $V_{\text {PYdidACKE }}=\frac{1}{3} V$.