Quantum Denoising Diffusion Models

TL;DR

Quantum Denoising Diffusion Models (QDDMs) integrate variational quantum circuits into diffusion-based image generation to reduce sampling time and parameter counts. The authors introduce two architectures, Q-Dense and QU-Net, and a unitary single-sampling scheme that compresses diffusion into a single unitary for one-shot generation, with demonstrations on MNIST, Fashion-MNIST, CIFAR-10 and IBMQ hardware. Across FID, SSIM, and PSNR, QDDMs with comparable parameter budgets outperform similar classical baselines and even approach the performance of larger classical models, while the unitary sampling framework shows substantial speedups. The work lays a foundation for quantum acceleration of generative diffusion, highlighting practical considerations for embedding, circuit design, and hardware feasibility in the NISQ era.

Abstract

In recent years, machine learning models like DALL-E, Craiyon, and Stable Diffusion have gained significant attention for their ability to generate high-resolution images from concise descriptions. Concurrently, quantum computing is showing promising advances, especially with quantum machine learning which capitalizes on quantum mechanics to meet the increasing computational requirements of traditional machine learning algorithms. This paper explores the integration of quantum machine learning and variational quantum circuits to augment the efficacy of diffusion-based image generation models. Specifically, we address two challenges of classical diffusion models: their low sampling speed and the extensive parameter requirements. We introduce two quantum diffusion models and benchmark their capabilities against their classical counterparts using MNIST digits, Fashion MNIST, and CIFAR-10. Our models surpass the classical models with similar parameter counts in terms of performance metrics FID, SSIM, and PSNR. Moreover, we introduce a consistency model unitary single sampling architecture that combines the diffusion procedure into a single step, enabling a fast one-step image generation.

Figures (13)

• Figure 1: Diffusion process ($\tau = 10$) of models Q-Dense, QDDPM qddpm, U-Net and Dense on MNIST digits. Samples from every second step are depicted.
• Figure 2: QU-Net architecture and quantum convolution, embedding a flattened slice into a dense quantum circuit.
• Figure 3: Unitary Single Sampling architecture.
• Figure 4: FID scores on MNIST 8x8 with guided models. $\tau$ denotes the diffusion steps. Lavender line illustrates larger U-Net capabilities for reference.
• Figure 5: Inpainting samples with a small mask on the top half, resetting the bottom after each of the 10 iterations.