# Quantum Denoising Diffusion Models

arXiv: https://arxiv.org/abs/2401.07049 · HTML: https://mlsanity.com/paper/2401.07049/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 25 of its 54 references that are in the map.
- First posted on arXiv 13 Jan 2024.

## Placed in

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

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [Deep Learning with Limited Numerical Precision](https://mlsanity.com/paper/1502.02551/) (2015)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [The Importance of Skip Connections in Biomedical Image Segmentation](https://mlsanity.com/paper/1608.04117/) (2016)
- [Fully Dense UNet for 2D Sparse Photoacoustic Tomography Artifact Removal](https://mlsanity.com/paper/1808.10848/) (2018)
- [An Introduction to Image Synthesis with Generative Adversarial Nets](https://mlsanity.com/paper/1803.04469/) (2018)
- [An Improved Evaluation Framework for Generative Adversarial Networks](https://mlsanity.com/paper/1803.07474/) (2018)
- [Improving Diffusion Model Efficiency Through Patching](https://mlsanity.com/paper/2207.04316/) (2022)
- [Accelerating Deep Convolutional Networks using low-precision and sparsity](https://mlsanity.com/paper/1610.00324/) (2016)
- [Improving Convergence for Quantum Variational Classifiers using Weight Re-Mapping](https://mlsanity.com/paper/2212.14807/) (2022)
- [The Holy Grail of Quantum Artificial Intelligence: Major Challenges in Accelerating the Machine Learning Pipeline](https://mlsanity.com/paper/2004.14035/) (2020)

## Built on by (most cited first, 11 of 11)

- [Quantum Machine Learning Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2407.20147/) (2024)
- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [Qandle: Accelerating State Vector Simulation Using Gate-Matrix Caching and Circuit Splitting](https://mlsanity.com/paper/2404.09213/) (2024)
- [Quantum Generative Models for Image Generation: Insights from MNIST and MedMNIST](https://mlsanity.com/paper/2504.00034/) (2025)
- [Local-Time Riemannian Score Matching on the Quantum Pure-State Manifold](https://mlsanity.com/paper/2605.03573/) (2026)
- [Quantum Diffusion Models for Few-Shot Learning](https://mlsanity.com/paper/2411.04217/) (2024)
- [Quantum King-Ring Domination in Chess: A QAOA Approach](https://mlsanity.com/paper/2601.00318/) (2026)
- [Intrinsic Flow Matching on Quantum Pure-State Manifolds with Phase-Aligned Transport](https://mlsanity.com/paper/2606.21256/) (2026)
- [An Hybrid Quantum-Classical Diffusion Model for Image Generation](https://mlsanity.com/paper/2607.07072/) (2026)
- [Quantum Circuits in Diffusion Models: A Fair-Comparison Study and a Mechanistic Analysis of Angle-Embedding Failures](https://mlsanity.com/paper/2607.09108/) (2026)
- [Quantum MeanFlow: single-shot generative sampling on NISQ hardware](https://mlsanity.com/paper/2609.02186/) (2026)

## Abstract (arXiv)

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.