Lytro released a video of a fashion model photographed with their light field camera. The camera appearance is blurred throughout the video except at the 1:26 mark where you can see a pixelated glimpse of the camera and its size:
Based on this picture, the camera appears not to be bigger than a regular DSLR.
The images form the photo shoot can be found on Lytro's website:
Here is the full video: