Quantum Circuits in Diffusion Models: A Fair-Comparison Study and a Mechanistic Analysis of Angle-Embedding Failures

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Original abstract

We study the integration of variational quantum circuits (VQCs) into diffusion models through a squeeze-and-excitation (SE) channel-modulation scaffold that isolates the quantum contribution. Using a role-matched classical control and multi-seed significance testing across DDPM and latent diffusion on MNIST and CIFAR-10, with a score-based NCSN study on MNIST, we find that quantum cores achieve comparable mean FID to the classical control across DDPM and latent diffusion, while paired sampling-seed tests for EfficientSU2 detect no statistically significant difference. Although the quantum cores use $4.5$--$9\times$ fewer core parameters than the role-matched control, parameter-matched classical controls attain comparable mean FID, so the experiments do not establish a quantum parameter-efficiency advantage. We further identify a structural failure in score-based NCSN: the unbounded score target, proportional to $1/σ$, drives angle-embedding inputs far beyond the $2π$ period of rotation gates, causing phase aliasing and collapse of the quantum modulator. A bounding transformation, $θ\leftarrow π\tanh(\cdot)$, maps inputs to the non-aliasing domain and substantially improves both quantum cores. Since all circuits are classically simulated at a few-qubit scale, we do not claim quantum advantage. Instead, the study provides a fair-comparison protocol for quantum-enhanced generative models and a mechanistic account of when and why angle embeddings fail.

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