Avoid caustics transparent shader (Cycles)


I have 6 object (stacked above each other floating just above the ‘floor’) fading from transparant to full diffused in to the scene by a keyframed mix shader mixing diff with transparant bsdf. Unfortunately I’m getting some unwanted caustics (as you can see on the exaggerated image here below) on the ground floor I would like to avoid. What is the proper way to fade object in to the scene?

thx a lot!