Diode Bridge with differential voltages. Transfer function
This is a 4-diode sampling bridge as used in sampling oscilloscopes.  With the +/-10V as shown the output follows the input.  If the polarities of the bias voltages are reversed the output is disconnected from the input.

In sampling oscilloscope use the output will have a small capacitor rather than a resistor to hold the sample value.

The bridge can do very fast sampling of the order of picoseconds if needed giving extremely the bandwidths.

With the input at zero the same current flows through both legs of the circuit and the output voltage will also be zero, any variation of the  input voltage requires that output voltage follow the input to maintain equilibrium.

kevin