An Hybrid Quantum-Classical Diffusion Model for Image Generation

2026-07-08

AI Summary

This work addresses the challenges of high encoding costs and computational complexity in simulating density operators when applying quantum diffusion models to high-dimensional classical data. To overcome these limitations, the authors propose a hybrid generative framework that first compresses the input data into a low-dimensional latent space using a classical autoencoder. Within this compressed space, they construct a mixed-state-based quantum denoising diffusion model and introduce a simplified reverse dynamics mechanism grounded in clean-state estimation. By integrating an analytical backpropagation rule, the framework enables efficient training and generation while substantially reducing quantum resource requirements. The approach demonstrates feasibility and effectiveness under limited qubit constraints, as validated through image generation tasks on the MNIST dataset.

Abstract

Quantum diffusion models provide a physics-consistent route to generative learning by formulating noising and denoising directly on quantum states. However, applying such models to classical high-dimensional data is constrained by the qubit cost of state encoding and the computational burden of simulating large density operators. We propose a scalable hybrid generative pipeline that combines a classical autoencoder for dimensionality reduction with a mixed-state quantum denoising diffusion probabilistic model (MSQuDDPM) operating in the learned latent space. The autoencoder compresses data into compact latent codes that can be embedded into a small-qubit Hilbert space, after which the quantum diffusion model learns a generative distribution over latent density operators and decodes samples back to the original domain. Algorithmically, we simplify the reverse dynamics by predicting an estimate of the clean state $ρ_0$ at timestep $t$ and computing the one-step reverse update via an analytic backward propagation rule, rather than learning an explicit predictor for $ρ_{t-1}$. We demonstrate the proposed approach on MNIST image generation and discuss how mixed-state quantum diffusion can serve as a practical backbone for hybrid quantum--classical generative modeling under realistic qubit budgets.

Problem

• quantum diffusion models
• image generation
• qubit cost
• high-dimensional data
• hybrid quantum-classical modeling

Innovation

• hybrid quantum-classical
• quantum diffusion model
• mixed-state denoising
• latent space embedding
• scalable generative modeling