There are a few gotchas in that statement though - for one, I didn't dive too far into the math, and I would assume that the convolutional algorithms as well as the underlying matrix functions may be different. But at the end of the day, you're approximating a complex function using an array of simple functions with different weights and scale factors. The other gotcha is that diffractive structures use monochromatic light, so it's probably not too useful in most normal situations with normal light sources.

I don't quite understand the mathematics of how it was trained, but they were able to discretize the geometry of those layers somehow into little 0.4mm pixels of "trainable diffractive neurons" and they simulated light transmission through the layers to compute a loss function.

I'm really surprised that this was computationally feasible. Simulation of light through the gratings must have been cheap enough as a function evaluation to train the network.