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

arXiv: https://arxiv.org/abs/2607.09108 · HTML: https://mlsanity.com/paper/2607.09108/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 12 of its 21 references that are in the map.
- First posted on arXiv 10 Jul 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 12 of 12)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Quantum generative adversarial networks](https://mlsanity.com/paper/1804.08641/) (2018)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Quantum-Noise-Driven Generative Diffusion Models](https://mlsanity.com/paper/2308.12013/) (2023)
- [Quantum Denoising Diffusion Models](https://mlsanity.com/paper/2401.07049/) (2024)

## Abstract (arXiv)

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× 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(·), 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.