To only have the background image change when the slide changes when you have added the same content to each slide, but it disappears briefly through slide transitions. This will make it stay. Add this css code into Divi > Theme Options > General > Custom CSS field.

 .et-pb-active-slide .et_pb_slide_description {
animation: 0s ease 0s normal none 1 running none !important;
-webkit-animation: none !important;
}