  Diffusion models generate new samples by progressively decreasing the noise
from the initially provided random distribution. This inference procedure
generally utilizes a trained neural network numerous times to obtain the final
output, creating significant latency and energy consumption on digital
electronic hardware such as GPUs. In this study, we demonstrate that the
propagation of a light beam through a semi-transparent medium can be programmed
to implement a denoising diffusion model on image samples. This framework
projects noisy image patterns through passive diffractive optical layers, which
collectively only transmit the predicted noise term in the image. The optical
transparent layers, which are trained with an online training approach,
backpropagating the error to the analytical model of the system, are passive
and kept the same across different steps of denoising. Hence this method
enables high-speed image generation with minimal power consumption, benefiting
from the bandwidth and energy efficiency of optical information processing.
