AD8130 output distortion under high-speed common-mode input transition

I am planning to use AD8130 to detect a small differential signal with a high-speed common-mode voltage.

Then AD8130's output shows a strange behavior in the rising edge. This is the two input voltage with the transition time of 8ns (right axis) and AD8130's output signal with a distortion (left axis).

The test circuit is just a standard differential amplifier setup with the gain of 2.

This phenomena becomes most visible when the two inputs are shorted and only a common-mode voltage is applied. Here is the circuit diagram of the new test circuit, while I expect no output voltage change with an input rising edge applied.

However, I got pulse-like output (left axis) at the transition of input voltage (right axis). The pulse-like outputs appear only when the rising time of the common-mode voltage is under 20ns.

This phenomena is nonlinear; i.e. the pulse-like output gets rapidly larger when the input amplitude increases. Thus it cannot be explained by the high-frequency CMRR of AD8130.

The output pulse appears regardless of the DC voltage level.

What is this behavior? How can I suppress this distortion? I do care about the transition response for my application.