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.

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.

This study introduces the Hybrid Diffraction Neural Network (HDNN), a novel architecture that incorporates matrix multiplication into DNNs, synergizing the benefits of conventional ONNs with those of DNNs to surmount the modulation limitations inherent in optical diffraction neural networks. Utilizing a singular phase modulation layer and an amplitude modulation layer, the trained neural network demonstrated remarkable accuracies of 96.39% and 89% in digit recognition tasks in simulation and experiment, respectively. Additionally, we develop the Binning Design (BD) method, which effectively mitigates the constraints imposed by sampling intervals on diffraction units, substantially streamlining experimental procedures. Furthermore, we propose an on-chip HDNN that not only employs a beam-splitting phase modulation layer for enhanced integration level but also significantly relaxes device fabrication requirements, replacing metasurfaces with relief surfaces designed by 1-bit quantization. Besides, we conceptualized an all-optical HDNN-assisted lesion detection network, achieving detection outcomes that were 100% aligned with simulation predictions.

Deep neural networks have achieved remarkable breakthroughs by leveraging multiple layers of data processing to extract hidden representations, albeit at the cost of large electronic computing power. To enhance energy efficiency and speed, the optical implementation of neural networks aims to harness the advantages of optical bandwidth and the energy efficiency of optical interconnections. In the absence of low-power optical nonlinearities, the challenge in the implementation of multilayer optical networks lies in realizing multiple optical layers without resorting to electronic components. In this study, we present a novel framework that uses multiple scattering that is capable of synthesizing programmable linear and nonlinear transformations concurrently at low optical power by leveraging the nonlinear relationship between the scattering potential, represented by data, and the scattered field. Theoretical and experimental investigations show that repeating the data by multiple scattering enables non-linear optical computing at low power continuous wave light.