Denoising diffusion models with optimized quantum implicit neural networks for image generation

Jiale Zhang, Xilong Che, Yuzhe Fan, Shun Peng, Geng Chen, Quangong Ma, Juncheng Hu

Abstract: Denoising Diffusion Models (DDMs) have attracted significant attention due to their capacity to generate diverse, high-quality samples in computer vision tasks, offering flexible architectures and straightforward training processes. While several studies have extended diffusion models to quantum domains, these approaches often rely on hybrid U-net architectures or mixed-state manipulations with trace-out measurements, which pose substantial challenges for implementation on current quantum hardware. To address these challenges, we introduce an Optimized Quantum Implicit Denoising Diffusion Model (OQIDDM), which combines our proposed Optimized Quantum Implicit Neural Networks (OQINNs) with Consistency Models. OQINNs optimizes the complex network structures inherent in existing Quantum Implicit Neural Networks. By leveraging OQINNs to model image data distributions over multiple timesteps and employing Consistency Models for O(1) sampling steps, our approach is better suited for deployment on noisy quantum hardware. Experimental results on the MNIST, Fashion-MNIST, and E-MNIST datasets demonstrate that OQIDDM outperforms existing quantum diffusion models in terms of image quality, while requiring far fewer parameters in the quantum neural network. Compared to state-of-the-art quantum generative adversarial networks (QGANs) and classical GANs, our model notably enhances image generation quality while substantially reducing training parameters. Additionally, we present experiments on facial image generation, marking the first application of quantum denoising diffusion models to complex datasets. Analysis of quantum noise effects, along with experimental results on three different superconducting quantum computers, further underscores the considerable potential of OQIDDM for quantum generative tasks.